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wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/104605612/Violation_of_Lee_Yang_circle_theorem_for_Ising_phase_transitions_on_complex_networks">Violation of Lee-Yang circle theorem for Ising phase transitions on complex networks</a></div><div class="wp-workCard_item"><span>EPL (Europhysics Letters)</span><span>, 2015</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="104605612"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span 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/></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/104605611/Fishers_scaling_relation_above_the_upper_critical_dimension">Fisher's scaling relation above the upper critical dimension</a></div><div class="wp-workCard_item"><span>EPL (Europhysics Letters)</span><span>, 2014</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="104605611"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="104605609"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/104605609/Site_diluted_Ising_model_in_four_dimensions"><img alt="Research paper thumbnail of Site-diluted Ising model in four dimensions" class="work-thumbnail" src="https://attachments.academia-assets.com/104290183/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/104605609/Site_diluted_Ising_model_in_four_dimensions">Site-diluted Ising model in four dimensions</a></div><div class="wp-workCard_item"><span>Physical Review E</span><span>, 2009</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="7e58229d83478198576e4a34b8bedd5d" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":104290183,"asset_id":104605609,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/104290183/download_file?st=MTczMjQ0OTY4MCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="104605609"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div 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"profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="100525319"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/100525319/Exponents"><img alt="Research paper thumbnail of Exponents" class="work-thumbnail" src="https://attachments.academia-assets.com/101324872/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/100525319/Exponents">Exponents</a></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="ab1c6ba6951b918b7c73c386e65c773b" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" 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are different to the classical ones. There followed the discovery of (now famous) scaling relations between the power-law critical exponents describing secondorder criticality. These scaling relations are of fundamental importance and now form a cornerstone of statistical mechanics. In certain circumstances, such scaling behaviour is modified by multiplicative logarithmic corrections. These are also characterized by critical exponents, analogous to the standard ones. Recently scaling relations between these logarithmic exponents have been established. Here, the theories associated with these advances are presented and expanded and the status of investigations into logarithmic corrections in a variety of models is reviewed.","publication_date":{"day":null,"month":null,"year":2016,"errors":{}},"grobid_abstract_attachment_id":101324872},"translated_abstract":null,"internal_url":"https://www.academia.edu/100525319/Exponents","translated_internal_url":"","created_at":"2023-04-21T00:36:02.970-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":57856370,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":101324872,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/101324872/thumbnails/1.jpg","file_name":"1205.4252.pdf","download_url":"https://www.academia.edu/attachments/101324872/download_file?st=MTczMjQ0OTY4MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Exponents.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/101324872/1205.4252-libre.pdf?1682063608=\u0026response-content-disposition=attachment%3B+filename%3DExponents.pdf\u0026Expires=1732453281\u0026Signature=W8gcJdGM6LkbxcMNnF7Hjt1Vp0~s2-p0o-17RQcRoPnOrzJsmRTJyfLKTF9foup5rVeaPKa6TDpeKlVjnMjhbj-BpJvmMuywC-rRIVGRUxKC7uMbARN8uFQlUvWo5cjYw5qJtxavmCPvH4wM6q9H5cHBxG~ECBg-pk4nVh6-LWx38FkI6louUJ37-E17Mf2osqqz7796O7gQnpoS388dSxmZQd2PhRNnUabS3xL~~FLE~Hmvm3JjR9pPRLO-JDqfoCCZ91KRzIrP3CHXLY7-hPLz1dToVtOLuG6~Vr7UpsdPvA8Ua5mOLShKsHHtuOCE5RMAgJjQP7eaH~F8SQjR3Q__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Exponents","translated_slug":"","page_count":48,"language":"en","content_type":"Work","owner":{"id":57856370,"first_name":"Ralph","middle_initials":null,"last_name":"Kenna","page_name":"KennaRalph","domain_name":"independent","created_at":"2016-12-09T08:34:18.408-08:00","display_name":"Ralph Kenna","url":"https://independent.academia.edu/KennaRalph"},"attachments":[{"id":101324872,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/101324872/thumbnails/1.jpg","file_name":"1205.4252.pdf","download_url":"https://www.academia.edu/attachments/101324872/download_file?st=MTczMjQ0OTY4MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Exponents.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/101324872/1205.4252-libre.pdf?1682063608=\u0026response-content-disposition=attachment%3B+filename%3DExponents.pdf\u0026Expires=1732453281\u0026Signature=W8gcJdGM6LkbxcMNnF7Hjt1Vp0~s2-p0o-17RQcRoPnOrzJsmRTJyfLKTF9foup5rVeaPKa6TDpeKlVjnMjhbj-BpJvmMuywC-rRIVGRUxKC7uMbARN8uFQlUvWo5cjYw5qJtxavmCPvH4wM6q9H5cHBxG~ECBg-pk4nVh6-LWx38FkI6louUJ37-E17Mf2osqqz7796O7gQnpoS388dSxmZQd2PhRNnUabS3xL~~FLE~Hmvm3JjR9pPRLO-JDqfoCCZ91KRzIrP3CHXLY7-hPLz1dToVtOLuG6~Vr7UpsdPvA8Ua5mOLShKsHHtuOCE5RMAgJjQP7eaH~F8SQjR3Q__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[],"urls":[{"id":30797138,"url":"http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.760.800\u0026rep=rep1\u0026type=pdf"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="86412258"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/86412258/Hyperscaling_above_the_upper_critical_dimension"><img alt="Research paper thumbnail of Hyperscaling above the upper critical dimension" class="work-thumbnail" src="https://attachments.academia-assets.com/90872013/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/86412258/Hyperscaling_above_the_upper_critical_dimension">Hyperscaling above the upper critical dimension</a></div><div class="wp-workCard_item"><span>Nuclear Physics B</span><span>, 2012</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="deb17797a287434c91c1e705b76a73e5" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":90872013,"asset_id":86412258,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/90872013/download_file?st=MTczMjQ0OTY4MSw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="86412258"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="86412258"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 86412258; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="78033772"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/78033772/O_ct_2_01_5_Partition_function_zeros_for_the_Ising_model_on_complete_graphs_and_on_annealed_scale_free_networks"><img alt="Research paper thumbnail of O ct 2 01 5 Partition function zeros for the Ising model on complete graphs and on annealed scale-free networks" class="work-thumbnail" src="https://attachments.academia-assets.com/85220221/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/78033772/O_ct_2_01_5_Partition_function_zeros_for_the_Ising_model_on_complete_graphs_and_on_annealed_scale_free_networks">O ct 2 01 5 Partition function zeros for the Ising model on complete graphs and on annealed scale-free networks</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We analyze the partition function of the Ising model on graphs of two different types: complete g...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We analyze the partition function of the Ising model on graphs of two different types: complete graphs, wherein all nodes are mutually linked and annealed scale-free networks for which the degree distribution decays as P (k) ∼ k. We are interested in zeros of the partition function in the cases of complex temperature or complex external field (Fisher and Lee-Yang zeros respectively). For the model on an annealed scale-free network, we find an integral representation for the partition function which, in the case λ &gt; 5, reproduces the zeros for the Ising model on a complete graph. For 3 &lt; λ &lt; 5 we derive the λ-dependent angle at which the Fisher zeros impact onto the real temperature axis. This, in turn, gives access to the λ-dependent universal values of the critical exponents and critical amplitudes ratios. Our analysis of the Lee-Yang zeros reveals a difference in their behaviour for the Ising model on a complete graph and on an annealed scale-free network when 3 &lt; λ &l...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="4b24a9b1e6617e68a8eee2ddb8d35b8a" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":85220221,"asset_id":78033772,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/85220221/download_file?st=MTczMjQ0OTY4MSw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="78033772"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="78033772"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 78033772; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=78033772]").text(description); $(".js-view-count[data-work-id=78033772]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 78033772; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='78033772']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 78033772, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "4b24a9b1e6617e68a8eee2ddb8d35b8a" } } $('.js-work-strip[data-work-id=78033772]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":78033772,"title":"O ct 2 01 5 Partition function zeros for the Ising model on complete graphs and on annealed scale-free networks","translated_title":"","metadata":{"abstract":"We analyze the partition function of the Ising model on graphs of two different types: complete graphs, wherein all nodes are mutually linked and annealed scale-free networks for which the degree distribution decays as P (k) ∼ k. We are interested in zeros of the partition function in the cases of complex temperature or complex external field (Fisher and Lee-Yang zeros respectively). For the model on an annealed scale-free network, we find an integral representation for the partition function which, in the case λ \u0026gt; 5, reproduces the zeros for the Ising model on a complete graph. For 3 \u0026lt; λ \u0026lt; 5 we derive the λ-dependent angle at which the Fisher zeros impact onto the real temperature axis. This, in turn, gives access to the λ-dependent universal values of the critical exponents and critical amplitudes ratios. Our analysis of the Lee-Yang zeros reveals a difference in their behaviour for the Ising model on a complete graph and on an annealed scale-free network when 3 \u0026lt; λ \u0026l...","publication_date":{"day":null,"month":null,"year":2015,"errors":{}}},"translated_abstract":"We analyze the partition function of the Ising model on graphs of two different types: complete graphs, wherein all nodes are mutually linked and annealed scale-free networks for which the degree distribution decays as P (k) ∼ k. We are interested in zeros of the partition function in the cases of complex temperature or complex external field (Fisher and Lee-Yang zeros respectively). For the model on an annealed scale-free network, we find an integral representation for the partition function which, in the case λ \u0026gt; 5, reproduces the zeros for the Ising model on a complete graph. For 3 \u0026lt; λ \u0026lt; 5 we derive the λ-dependent angle at which the Fisher zeros impact onto the real temperature axis. This, in turn, gives access to the λ-dependent universal values of the critical exponents and critical amplitudes ratios. Our analysis of the Lee-Yang zeros reveals a difference in their behaviour for the Ising model on a complete graph and on an annealed scale-free network when 3 \u0026lt; λ \u0026l...","internal_url":"https://www.academia.edu/78033772/O_ct_2_01_5_Partition_function_zeros_for_the_Ising_model_on_complete_graphs_and_on_annealed_scale_free_networks","translated_internal_url":"","created_at":"2022-04-30T04:19:26.364-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":57856370,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":85220221,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/85220221/thumbnails/1.jpg","file_name":"1510.pdf","download_url":"https://www.academia.edu/attachments/85220221/download_file?st=MTczMjQ0OTY4MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"O_ct_2_01_5_Partition_function_zeros_for.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/85220221/1510-libre.pdf?1651318778=\u0026response-content-disposition=attachment%3B+filename%3DO_ct_2_01_5_Partition_function_zeros_for.pdf\u0026Expires=1732453281\u0026Signature=gKfH-BBoOmkd21et8Ih5RAKJ1yK9A~-4pCyPHgLKaJd6XcCt~xsYEgIM5xVceLzvrkVBQ5hP0IHn2I~h-DZOKTLIQ2UT7RL809dONi0FkW1lb-Pa4qxsG8sDPVzdotJzjQ4H1tcVX5~JHT0HrVj23sYbJ0dtKy2NTE3UqL8YDldzWHyKKT6KhrQNBZZXAtzUablYA9rOoA2lTb5EDtAqHmdibpgcwdVLWS22Qgc8etLzvHHlrfDrHKVkEQvtMXIUTxkOjXKdIvAtWABHiobuORFTfvqkxIemmC15-RDnTVOX0phCUEG9v59oFg3rTwDiy8YAOppo6Za1o1y~rqSCkQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"O_ct_2_01_5_Partition_function_zeros_for_the_Ising_model_on_complete_graphs_and_on_annealed_scale_free_networks","translated_slug":"","page_count":36,"language":"en","content_type":"Work","owner":{"id":57856370,"first_name":"Ralph","middle_initials":null,"last_name":"Kenna","page_name":"KennaRalph","domain_name":"independent","created_at":"2016-12-09T08:34:18.408-08:00","display_name":"Ralph Kenna","url":"https://independent.academia.edu/KennaRalph"},"attachments":[{"id":85220221,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/85220221/thumbnails/1.jpg","file_name":"1510.pdf","download_url":"https://www.academia.edu/attachments/85220221/download_file?st=MTczMjQ0OTY4MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"O_ct_2_01_5_Partition_function_zeros_for.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/85220221/1510-libre.pdf?1651318778=\u0026response-content-disposition=attachment%3B+filename%3DO_ct_2_01_5_Partition_function_zeros_for.pdf\u0026Expires=1732453281\u0026Signature=gKfH-BBoOmkd21et8Ih5RAKJ1yK9A~-4pCyPHgLKaJd6XcCt~xsYEgIM5xVceLzvrkVBQ5hP0IHn2I~h-DZOKTLIQ2UT7RL809dONi0FkW1lb-Pa4qxsG8sDPVzdotJzjQ4H1tcVX5~JHT0HrVj23sYbJ0dtKy2NTE3UqL8YDldzWHyKKT6KhrQNBZZXAtzUablYA9rOoA2lTb5EDtAqHmdibpgcwdVLWS22Qgc8etLzvHHlrfDrHKVkEQvtMXIUTxkOjXKdIvAtWABHiobuORFTfvqkxIemmC15-RDnTVOX0phCUEG9v59oFg3rTwDiy8YAOppo6Za1o1y~rqSCkQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"},{"id":85220222,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/85220222/thumbnails/1.jpg","file_name":"1510.pdf","download_url":"https://www.academia.edu/attachments/85220222/download_file","bulk_download_file_name":"O_ct_2_01_5_Partition_function_zeros_for.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/85220222/1510-libre.pdf?1651318775=\u0026response-content-disposition=attachment%3B+filename%3DO_ct_2_01_5_Partition_function_zeros_for.pdf\u0026Expires=1732453281\u0026Signature=BaxNCdMxFj9V3dR4NgubXVbMlwvA-p8HLXxpBaWz3Hi0A-g~wfqd46UOd3OcbC7a~RAwJjQijXZ3VHjj3jIK4mt6e37mROwyENkiMdrXnrjVgUwG45IaM3cR311Bkym9Agw19nwtqZlBabn7csuT2rsC96tMz83PTMW~MU5z79ECKcNBjGmke0DCvgrUzKNGefTThPFFYtkwhz2QVQYw4QdyQHEksLsh6Kt~egkiugDce7n55ICZius5TITRXhiw--fCM48424G3RK6DNgUOz0ZsqAe~sOJhbFlB0ucLkB-pv7stkePA2Rdsx5frBOTa47v95OSnb-t94ijL50knjA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[],"urls":[{"id":20060977,"url":"http://export.arxiv.org/pdf/1510.00534"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="78033771"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/78033771/The_two_point_resistance_of_fan_networks"><img alt="Research paper thumbnail of The two-point resistance of fan networks" class="work-thumbnail" src="https://attachments.academia-assets.com/85220218/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/78033771/The_two_point_resistance_of_fan_networks">The two-point resistance of fan networks</a></div><div class="wp-workCard_item"><span>arXiv: Statistical Mechanics</span><span>, 2014</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The problem of the two-point resistance in various networks has recently received considerable at...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The problem of the two-point resistance in various networks has recently received considerable attention. Here we consider the problem on a fan-resistor network, which is a segment of the cobweb network. Using a recently developed approach, we obtain the exact resistance between two arbitrary nodes on such a network. As a byproduct, the analysis also delivers the solution of the spanning tree problem on the fan network.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="4a981843ac7a3d8b9265ca1c3a29417b" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":85220218,"asset_id":78033771,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/85220218/download_file?st=MTczMjQ0OTY4MSw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="78033771"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="78033771"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 78033771; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=78033771]").text(description); $(".js-view-count[data-work-id=78033771]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 78033771; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='78033771']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 78033771, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "4a981843ac7a3d8b9265ca1c3a29417b" } } $('.js-work-strip[data-work-id=78033771]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":78033771,"title":"The two-point resistance of fan networks","translated_title":"","metadata":{"abstract":"The problem of the two-point resistance in various networks has recently received considerable attention. Here we consider the problem on a fan-resistor network, which is a segment of the cobweb network. Using a recently developed approach, we obtain the exact resistance between two arbitrary nodes on such a network. As a byproduct, the analysis also delivers the solution of the spanning tree problem on the fan network.","publication_date":{"day":null,"month":null,"year":2014,"errors":{}},"publication_name":"arXiv: Statistical Mechanics"},"translated_abstract":"The problem of the two-point resistance in various networks has recently received considerable attention. Here we consider the problem on a fan-resistor network, which is a segment of the cobweb network. Using a recently developed approach, we obtain the exact resistance between two arbitrary nodes on such a network. As a byproduct, the analysis also delivers the solution of the spanning tree problem on the fan network.","internal_url":"https://www.academia.edu/78033771/The_two_point_resistance_of_fan_networks","translated_internal_url":"","created_at":"2022-04-30T04:19:26.176-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":57856370,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":85220218,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/85220218/thumbnails/1.jpg","file_name":"1401.4463v1.pdf","download_url":"https://www.academia.edu/attachments/85220218/download_file?st=MTczMjQ0OTY4MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"The_two_point_resistance_of_fan_networks.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/85220218/1401.4463v1-libre.pdf?1651318768=\u0026response-content-disposition=attachment%3B+filename%3DThe_two_point_resistance_of_fan_networks.pdf\u0026Expires=1732453281\u0026Signature=CZkreByZED7WO0tY3j-mep~GKyoljmidPWGX9H3c~fvCJj4j23E3YPFq1Tan294sq2HK6kgBclghHyclRSntDnRol92o604pJv7XBnRhcVlwbERpGtg6-DqkrU0nF42HPfuUcYuBlzA0DGrlewnFEtsMTSEdvxTiCSWgob8-KK91ms2eXlJPfinkMzRIpWyCCIAkAFzt9WWTF~eLnf6oAo39n0yHnQ7IP-uyLoYQviXWhgnj7xStFzwNFKsa11uRvzO~DYuua75ddmUgrd4b~yEpAmDBerX3UzGqdtPn0tRatPGC66jroXW-sbuPfispSiS9HovrYWQQ47C6tSu1cw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"The_two_point_resistance_of_fan_networks","translated_slug":"","page_count":10,"language":"en","content_type":"Work","owner":{"id":57856370,"first_name":"Ralph","middle_initials":null,"last_name":"Kenna","page_name":"KennaRalph","domain_name":"independent","created_at":"2016-12-09T08:34:18.408-08:00","display_name":"Ralph Kenna","url":"https://independent.academia.edu/KennaRalph"},"attachments":[{"id":85220218,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/85220218/thumbnails/1.jpg","file_name":"1401.4463v1.pdf","download_url":"https://www.academia.edu/attachments/85220218/download_file?st=MTczMjQ0OTY4MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"The_two_point_resistance_of_fan_networks.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/85220218/1401.4463v1-libre.pdf?1651318768=\u0026response-content-disposition=attachment%3B+filename%3DThe_two_point_resistance_of_fan_networks.pdf\u0026Expires=1732453281\u0026Signature=CZkreByZED7WO0tY3j-mep~GKyoljmidPWGX9H3c~fvCJj4j23E3YPFq1Tan294sq2HK6kgBclghHyclRSntDnRol92o604pJv7XBnRhcVlwbERpGtg6-DqkrU0nF42HPfuUcYuBlzA0DGrlewnFEtsMTSEdvxTiCSWgob8-KK91ms2eXlJPfinkMzRIpWyCCIAkAFzt9WWTF~eLnf6oAo39n0yHnQ7IP-uyLoYQviXWhgnj7xStFzwNFKsa11uRvzO~DYuua75ddmUgrd4b~yEpAmDBerX3UzGqdtPn0tRatPGC66jroXW-sbuPfispSiS9HovrYWQQ47C6tSu1cw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":498,"name":"Physics","url":"https://www.academia.edu/Documents/in/Physics"}],"urls":[{"id":20060976,"url":"https://arxiv.org/pdf/1401.4463v1.pdf"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="78033770"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/78033770/Generalized_Ising_Model_on_a_Scale_Free_Network_An_Interplay_of_Power_Laws"><img alt="Research paper thumbnail of Generalized Ising Model on a Scale-Free Network: An Interplay of Power Laws" class="work-thumbnail" src="https://attachments.academia-assets.com/85220215/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/78033770/Generalized_Ising_Model_on_a_Scale_Free_Network_An_Interplay_of_Power_Laws">Generalized Ising Model on a Scale-Free Network: An Interplay of Power Laws</a></div><div class="wp-workCard_item"><span>Entropy</span><span>, 2021</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We consider a recently introduced generalization of the Ising model in which individual spin stre...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We consider a recently introduced generalization of the Ising model in which individual spin strength can vary. The model is intended for analysis of ordering in systems comprising agents which, although matching in their binarity (i.e., maintaining the iconic Ising features of ‘+’ or ‘−’, ‘up’ or ‘down’, ‘yes’ or ‘no’), differ in their strength. To investigate the interplay between variable properties of nodes and interactions between them, we study the model on a complex network where both the spin strength and degree distributions are governed by power laws. We show that in the annealed network approximation, thermodynamic functions of the model are self-averaging and we obtain an exact solution for the partition function. This allows us derive the leading temperature and field dependencies of thermodynamic functions, their critical behavior, and logarithmic corrections at the interface of different phases. We find the delicate interplay of the two power laws leads to new univers...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="622910e8149f909841c4efdbb1b5592f" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":85220215,"asset_id":78033770,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/85220215/download_file?st=MTczMjQ0OTY4Miw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="78033770"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="78033770"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 78033770; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=78033770]").text(description); $(".js-view-count[data-work-id=78033770]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 78033770; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='78033770']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 78033770, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "622910e8149f909841c4efdbb1b5592f" } } $('.js-work-strip[data-work-id=78033770]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":78033770,"title":"Generalized Ising Model on a Scale-Free Network: An Interplay of Power Laws","translated_title":"","metadata":{"abstract":"We consider a recently introduced generalization of the Ising model in which individual spin strength can vary. 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="78033769"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/78033769/Narrative_structure_ofA_Song_of_Ice_and_Firecreates_a_fictional_world_with_realistic_measures_of_social_complexity"><img alt="Research paper thumbnail of Narrative structure ofA Song of Ice and Firecreates a fictional world with realistic measures of social complexity" class="work-thumbnail" src="https://attachments.academia-assets.com/85220363/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/78033769/Narrative_structure_ofA_Song_of_Ice_and_Firecreates_a_fictional_world_with_realistic_measures_of_social_complexity">Narrative structure ofA Song of Ice and Firecreates a fictional world with realistic measures of social complexity</a></div><div class="wp-workCard_item"><span>Proceedings of the National Academy of Sciences</span><span>, 2020</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Network science and data analytics are used to quantify static and dynamic structures in George R...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Network science and data analytics are used to quantify static and dynamic structures in George R. R. Martin’s epic novels,A Song of Ice and Fire, works noted for their scale and complexity. By tracking the network of character interactions as the story unfolds, it is found that structural properties remain approximately stable and comparable to real-world social networks. Furthermore, the degrees of the most connected characters reflect a cognitive limit on the number of concurrent social connections that humans tend to maintain. We also analyze the distribution of time intervals between significant deaths measured with respect to the in-story timeline. These are consistent with power-law distributions commonly found in interevent times for a range of nonviolent human activities in the real world. We propose that structural features in the narrative that are reflected in our actual social world help readers to follow and to relate to the story, despite its sprawling extent. It is a...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="8e27c96928e6839d5321cc784b14937b" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":85220363,"asset_id":78033769,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/85220363/download_file?st=MTczMjQ0OTY4Miw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="78033769"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="78033769"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 78033769; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=78033769]").text(description); $(".js-view-count[data-work-id=78033769]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 78033769; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='78033769']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 78033769, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "8e27c96928e6839d5321cc784b14937b" } } $('.js-work-strip[data-work-id=78033769]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":78033769,"title":"Narrative structure ofA Song of Ice and Firecreates a fictional world with realistic measures of social complexity","translated_title":"","metadata":{"abstract":"Network science and data analytics are used to quantify static and dynamic structures in George R. R. Martin’s epic novels,A Song of Ice and Fire, works noted for their scale and complexity. By tracking the network of character interactions as the story unfolds, it is found that structural properties remain approximately stable and comparable to real-world social networks. Furthermore, the degrees of the most connected characters reflect a cognitive limit on the number of concurrent social connections that humans tend to maintain. We also analyze the distribution of time intervals between significant deaths measured with respect to the in-story timeline. These are consistent with power-law distributions commonly found in interevent times for a range of nonviolent human activities in the real world. We propose that structural features in the narrative that are reflected in our actual social world help readers to follow and to relate to the story, despite its sprawling extent. It is a...","publisher":"Proceedings of the National Academy of Sciences","publication_date":{"day":null,"month":null,"year":2020,"errors":{}},"publication_name":"Proceedings of the National Academy of Sciences"},"translated_abstract":"Network science and data analytics are used to quantify static and dynamic structures in George R. R. Martin’s epic novels,A Song of Ice and Fire, works noted for their scale and complexity. By tracking the network of character interactions as the story unfolds, it is found that structural properties remain approximately stable and comparable to real-world social networks. Furthermore, the degrees of the most connected characters reflect a cognitive limit on the number of concurrent social connections that humans tend to maintain. We also analyze the distribution of time intervals between significant deaths measured with respect to the in-story timeline. These are consistent with power-law distributions commonly found in interevent times for a range of nonviolent human activities in the real world. We propose that structural features in the narrative that are reflected in our actual social world help readers to follow and to relate to the story, despite its sprawling extent. It is a...","internal_url":"https://www.academia.edu/78033769/Narrative_structure_ofA_Song_of_Ice_and_Firecreates_a_fictional_world_with_realistic_measures_of_social_complexity","translated_internal_url":"","created_at":"2022-04-30T04:19:25.774-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":57856370,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":85220363,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/85220363/thumbnails/1.jpg","file_name":"2012.01783v1.pdf","download_url":"https://www.academia.edu/attachments/85220363/download_file?st=MTczMjQ0OTY4Miw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Narrative_structure_ofA_Song_of_Ice_and.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/85220363/2012.01783v1-libre.pdf?1651318769=\u0026response-content-disposition=attachment%3B+filename%3DNarrative_structure_ofA_Song_of_Ice_and.pdf\u0026Expires=1732453282\u0026Signature=BbbsMeNTrh10Wkql7YWRAf3MREy95NDDkY1sPM7YTwWiMZgPPWU7i01DaJ~ny9wHkxR3gYuSeh4yxccVs9wO5SNpMNsay7u4~Gv2SYeV3XajcUz9p5nvjUhD-p6mDXL~PLAZUwLNLsDjYcCVmjcyaZAP42SjABH-4Oa5fuA5siMHadcchNrYWUybr0LDS9lsTEmqPFc7D-Vr93zu2NRzdYaJoPA3PVJV-JrKCS~dHo9RJM2L5lDSJCjhT65PDe880yjolhCQ5JZbUiqtRMQzKZkKFglxFfdDAqlhtb5LmCqXtW~UX1n1-O1TlO9UErF0opB~yV82SSiq1f3u3bGGng__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Narrative_structure_ofA_Song_of_Ice_and_Firecreates_a_fictional_world_with_realistic_measures_of_social_complexity","translated_slug":"","page_count":15,"language":"en","content_type":"Work","owner":{"id":57856370,"first_name":"Ralph","middle_initials":null,"last_name":"Kenna","page_name":"KennaRalph","domain_name":"independent","created_at":"2016-12-09T08:34:18.408-08:00","display_name":"Ralph Kenna","url":"https://independent.academia.edu/KennaRalph"},"attachments":[{"id":85220363,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/85220363/thumbnails/1.jpg","file_name":"2012.01783v1.pdf","download_url":"https://www.academia.edu/attachments/85220363/download_file?st=MTczMjQ0OTY4Miw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Narrative_structure_ofA_Song_of_Ice_and.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/85220363/2012.01783v1-libre.pdf?1651318769=\u0026response-content-disposition=attachment%3B+filename%3DNarrative_structure_ofA_Song_of_Ice_and.pdf\u0026Expires=1732453282\u0026Signature=BbbsMeNTrh10Wkql7YWRAf3MREy95NDDkY1sPM7YTwWiMZgPPWU7i01DaJ~ny9wHkxR3gYuSeh4yxccVs9wO5SNpMNsay7u4~Gv2SYeV3XajcUz9p5nvjUhD-p6mDXL~PLAZUwLNLsDjYcCVmjcyaZAP42SjABH-4Oa5fuA5siMHadcchNrYWUybr0LDS9lsTEmqPFc7D-Vr93zu2NRzdYaJoPA3PVJV-JrKCS~dHo9RJM2L5lDSJCjhT65PDe880yjolhCQ5JZbUiqtRMQzKZkKFglxFfdDAqlhtb5LmCqXtW~UX1n1-O1TlO9UErF0opB~yV82SSiq1f3u3bGGng__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":128,"name":"History","url":"https://www.academia.edu/Documents/in/History"},{"id":498,"name":"Physics","url":"https://www.academia.edu/Documents/in/Physics"},{"id":26327,"name":"Medicine","url":"https://www.academia.edu/Documents/in/Medicine"},{"id":28235,"name":"Multidisciplinary","url":"https://www.academia.edu/Documents/in/Multidisciplinary"},{"id":2068869,"name":"Academy of Sciences and Letters","url":"https://www.academia.edu/Documents/in/Academy_of_Sciences_and_Letters"}],"urls":[{"id":20060974,"url":"https://syndication.highwire.org/content/doi/10.1073/pnas.2006465117"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="78033768"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/78033768/Use_of_the_Complex_Zeros_of_the_Partition_Function_to_Investigate_the_Critical_Behavior_of_the_Generalized_Interacting_Self_Avoiding_Trail_Model"><img alt="Research paper thumbnail of Use of the Complex Zeros of the Partition Function to Investigate the Critical Behavior of the Generalized Interacting Self-Avoiding Trail Model" class="work-thumbnail" src="https://attachments.academia-assets.com/85220212/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/78033768/Use_of_the_Complex_Zeros_of_the_Partition_Function_to_Investigate_the_Critical_Behavior_of_the_Generalized_Interacting_Self_Avoiding_Trail_Model">Use of the Complex Zeros of the Partition Function to Investigate the Critical Behavior of the Generalized Interacting Self-Avoiding Trail Model</a></div><div class="wp-workCard_item"><span>Entropy</span><span>, 2019</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The complex zeros of the canonical (fixed walk-length) partition function are calculated for both...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The complex zeros of the canonical (fixed walk-length) partition function are calculated for both the self-avoiding trails model and the vertex-interacting self-avoiding walk model, both in bulk and in the presence of an attractive surface. The finite-size behavior of the zeros is used to estimate the location of phase transitions: the collapse transition in the bulk and the adsorption transition in the presence of a surface. The bulk and surface cross-over exponents, ϕ and ϕ S , are estimated from the scaling behavior of the leading partition function zeros.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="bcda17b77e015702b545d10c177f4612" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":85220212,"asset_id":78033768,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/85220212/download_file?st=MTczMjQ0OTY4Miw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="78033768"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="78033768"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 78033768; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=78033768]").text(description); $(".js-view-count[data-work-id=78033768]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 78033768; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='78033768']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 78033768, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "bcda17b77e015702b545d10c177f4612" } } $('.js-work-strip[data-work-id=78033768]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":78033768,"title":"Use of the Complex Zeros of the Partition Function to Investigate the Critical Behavior of the Generalized Interacting Self-Avoiding Trail Model","translated_title":"","metadata":{"abstract":"The complex zeros of the canonical (fixed walk-length) partition function are calculated for both the self-avoiding trails model and the vertex-interacting self-avoiding walk model, both in bulk and in the presence of an attractive surface. 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="78033763"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/78033763/Comparison_of_methods_to_determine_point_to_point_resistance_in_nearly_rectangular_networks_with_application_to_a_hammock_network"><img alt="Research paper thumbnail of Comparison of methods to determine point-to-point resistance in nearly rectangular networks with application to a 'hammock' network" class="work-thumbnail" src="https://attachments.academia-assets.com/85220358/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/78033763/Comparison_of_methods_to_determine_point_to_point_resistance_in_nearly_rectangular_networks_with_application_to_a_hammock_network">Comparison of methods to determine point-to-point resistance in nearly rectangular networks with application to a 'hammock' network</a></div><div class="wp-workCard_item"><span>Royal Society open science</span><span>, 2015</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Considerable progress has recently been made in the development of techniques to exactly determin...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Considerable progress has recently been made in the development of techniques to exactly determine two-point resistances in networks of various topologies. In particular, two types of method have emerged. One is based on potentials and the evaluation of eigenvalues and eigenvectors of the Laplacian matrix associated with the network or its minors. The second method is based on a recurrence relation associated with the distribution of currents in the network. 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In particular, two types of method have emerged. One is based on potentials and the evaluation of eigenvalues and eigenvectors of the Laplacian matrix associated with the network or its minors. The second method is based on a recurrence relation associated with the distribution of currents in the network. Here, these methods are compared and used to determine the resistance distances between any two nodes of a network with topology of a hammock.","publication_date":{"day":null,"month":null,"year":2015,"errors":{}},"publication_name":"Royal Society open science"},"translated_abstract":"Considerable progress has recently been made in the development of techniques to exactly determine two-point resistances in networks of various topologies. In particular, two types of method have emerged. One is based on potentials and the evaluation of eigenvalues and eigenvectors of the Laplacian matrix associated with the network or its minors. 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data-click-track="profile-work-strip-title" href="https://www.academia.edu/104605612/Violation_of_Lee_Yang_circle_theorem_for_Ising_phase_transitions_on_complex_networks">Violation of Lee-Yang circle theorem for Ising phase transitions on complex networks</a></div><div class="wp-workCard_item"><span>EPL (Europhysics Letters)</span><span>, 2015</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="104605612"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" 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There followed the discovery of (now famous) scaling relations between the power-law critical exponents describing secondorder criticality. These scaling relations are of fundamental importance and now form a cornerstone of statistical mechanics. In certain circumstances, such scaling behaviour is modified by multiplicative logarithmic corrections. These are also characterized by critical exponents, analogous to the standard ones. Recently scaling relations between these logarithmic exponents have been established. Here, the theories associated with these advances are presented and expanded and the status of investigations into logarithmic corrections in a variety of models is reviewed.","publication_date":{"day":null,"month":null,"year":2016,"errors":{}},"grobid_abstract_attachment_id":101324872},"translated_abstract":null,"internal_url":"https://www.academia.edu/100525319/Exponents","translated_internal_url":"","created_at":"2023-04-21T00:36:02.970-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":57856370,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":101324872,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/101324872/thumbnails/1.jpg","file_name":"1205.4252.pdf","download_url":"https://www.academia.edu/attachments/101324872/download_file?st=MTczMjQ0OTY4Myw4LjIyMi4yMDguMTQ2&st=MTczMjQ0OTY4MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Exponents.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/101324872/1205.4252-libre.pdf?1682063608=\u0026response-content-disposition=attachment%3B+filename%3DExponents.pdf\u0026Expires=1732453281\u0026Signature=W8gcJdGM6LkbxcMNnF7Hjt1Vp0~s2-p0o-17RQcRoPnOrzJsmRTJyfLKTF9foup5rVeaPKa6TDpeKlVjnMjhbj-BpJvmMuywC-rRIVGRUxKC7uMbARN8uFQlUvWo5cjYw5qJtxavmCPvH4wM6q9H5cHBxG~ECBg-pk4nVh6-LWx38FkI6louUJ37-E17Mf2osqqz7796O7gQnpoS388dSxmZQd2PhRNnUabS3xL~~FLE~Hmvm3JjR9pPRLO-JDqfoCCZ91KRzIrP3CHXLY7-hPLz1dToVtOLuG6~Vr7UpsdPvA8Ua5mOLShKsHHtuOCE5RMAgJjQP7eaH~F8SQjR3Q__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Exponents","translated_slug":"","page_count":48,"language":"en","content_type":"Work","owner":{"id":57856370,"first_name":"Ralph","middle_initials":null,"last_name":"Kenna","page_name":"KennaRalph","domain_name":"independent","created_at":"2016-12-09T08:34:18.408-08:00","display_name":"Ralph Kenna","url":"https://independent.academia.edu/KennaRalph"},"attachments":[{"id":101324872,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/101324872/thumbnails/1.jpg","file_name":"1205.4252.pdf","download_url":"https://www.academia.edu/attachments/101324872/download_file?st=MTczMjQ0OTY4Myw4LjIyMi4yMDguMTQ2&st=MTczMjQ0OTY4MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Exponents.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/101324872/1205.4252-libre.pdf?1682063608=\u0026response-content-disposition=attachment%3B+filename%3DExponents.pdf\u0026Expires=1732453281\u0026Signature=W8gcJdGM6LkbxcMNnF7Hjt1Vp0~s2-p0o-17RQcRoPnOrzJsmRTJyfLKTF9foup5rVeaPKa6TDpeKlVjnMjhbj-BpJvmMuywC-rRIVGRUxKC7uMbARN8uFQlUvWo5cjYw5qJtxavmCPvH4wM6q9H5cHBxG~ECBg-pk4nVh6-LWx38FkI6louUJ37-E17Mf2osqqz7796O7gQnpoS388dSxmZQd2PhRNnUabS3xL~~FLE~Hmvm3JjR9pPRLO-JDqfoCCZ91KRzIrP3CHXLY7-hPLz1dToVtOLuG6~Vr7UpsdPvA8Ua5mOLShKsHHtuOCE5RMAgJjQP7eaH~F8SQjR3Q__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[],"urls":[{"id":30797138,"url":"http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.760.800\u0026rep=rep1\u0026type=pdf"}]}, dispatcherData: dispatcherData }); 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="78033772"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/78033772/O_ct_2_01_5_Partition_function_zeros_for_the_Ising_model_on_complete_graphs_and_on_annealed_scale_free_networks"><img alt="Research paper thumbnail of O ct 2 01 5 Partition function zeros for the Ising model on complete graphs and on annealed scale-free networks" class="work-thumbnail" src="https://attachments.academia-assets.com/85220221/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/78033772/O_ct_2_01_5_Partition_function_zeros_for_the_Ising_model_on_complete_graphs_and_on_annealed_scale_free_networks">O ct 2 01 5 Partition function zeros for the Ising model on complete graphs and on annealed scale-free networks</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We analyze the partition function of the Ising model on graphs of two different types: complete g...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We analyze the partition function of the Ising model on graphs of two different types: complete graphs, wherein all nodes are mutually linked and annealed scale-free networks for which the degree distribution decays as P (k) ∼ k. We are interested in zeros of the partition function in the cases of complex temperature or complex external field (Fisher and Lee-Yang zeros respectively). For the model on an annealed scale-free network, we find an integral representation for the partition function which, in the case λ &gt; 5, reproduces the zeros for the Ising model on a complete graph. For 3 &lt; λ &lt; 5 we derive the λ-dependent angle at which the Fisher zeros impact onto the real temperature axis. This, in turn, gives access to the λ-dependent universal values of the critical exponents and critical amplitudes ratios. Our analysis of the Lee-Yang zeros reveals a difference in their behaviour for the Ising model on a complete graph and on an annealed scale-free network when 3 &lt; λ &l...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="4b24a9b1e6617e68a8eee2ddb8d35b8a" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":85220221,"asset_id":78033772,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/85220221/download_file?st=MTczMjQ0OTY4Myw4LjIyMi4yMDguMTQ2&st=MTczMjQ0OTY4MSw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="78033772"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="78033772"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 78033772; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=78033772]").text(description); $(".js-view-count[data-work-id=78033772]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 78033772; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='78033772']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 78033772, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "4b24a9b1e6617e68a8eee2ddb8d35b8a" } } $('.js-work-strip[data-work-id=78033772]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":78033772,"title":"O ct 2 01 5 Partition function zeros for the Ising model on complete graphs and on annealed scale-free networks","translated_title":"","metadata":{"abstract":"We analyze the partition function of the Ising model on graphs of two different types: complete graphs, wherein all nodes are mutually linked and annealed scale-free networks for which the degree distribution decays as P (k) ∼ k. We are interested in zeros of the partition function in the cases of complex temperature or complex external field (Fisher and Lee-Yang zeros respectively). For the model on an annealed scale-free network, we find an integral representation for the partition function which, in the case λ \u0026gt; 5, reproduces the zeros for the Ising model on a complete graph. For 3 \u0026lt; λ \u0026lt; 5 we derive the λ-dependent angle at which the Fisher zeros impact onto the real temperature axis. This, in turn, gives access to the λ-dependent universal values of the critical exponents and critical amplitudes ratios. Our analysis of the Lee-Yang zeros reveals a difference in their behaviour for the Ising model on a complete graph and on an annealed scale-free network when 3 \u0026lt; λ \u0026l...","publication_date":{"day":null,"month":null,"year":2015,"errors":{}}},"translated_abstract":"We analyze the partition function of the Ising model on graphs of two different types: complete graphs, wherein all nodes are mutually linked and annealed scale-free networks for which the degree distribution decays as P (k) ∼ k. We are interested in zeros of the partition function in the cases of complex temperature or complex external field (Fisher and Lee-Yang zeros respectively). For the model on an annealed scale-free network, we find an integral representation for the partition function which, in the case λ \u0026gt; 5, reproduces the zeros for the Ising model on a complete graph. For 3 \u0026lt; λ \u0026lt; 5 we derive the λ-dependent angle at which the Fisher zeros impact onto the real temperature axis. This, in turn, gives access to the λ-dependent universal values of the critical exponents and critical amplitudes ratios. Our analysis of the Lee-Yang zeros reveals a difference in their behaviour for the Ising model on a complete graph and on an annealed scale-free network when 3 \u0026lt; λ \u0026l...","internal_url":"https://www.academia.edu/78033772/O_ct_2_01_5_Partition_function_zeros_for_the_Ising_model_on_complete_graphs_and_on_annealed_scale_free_networks","translated_internal_url":"","created_at":"2022-04-30T04:19:26.364-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":57856370,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":85220221,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/85220221/thumbnails/1.jpg","file_name":"1510.pdf","download_url":"https://www.academia.edu/attachments/85220221/download_file?st=MTczMjQ0OTY4Myw4LjIyMi4yMDguMTQ2&st=MTczMjQ0OTY4MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"O_ct_2_01_5_Partition_function_zeros_for.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/85220221/1510-libre.pdf?1651318778=\u0026response-content-disposition=attachment%3B+filename%3DO_ct_2_01_5_Partition_function_zeros_for.pdf\u0026Expires=1732453281\u0026Signature=gKfH-BBoOmkd21et8Ih5RAKJ1yK9A~-4pCyPHgLKaJd6XcCt~xsYEgIM5xVceLzvrkVBQ5hP0IHn2I~h-DZOKTLIQ2UT7RL809dONi0FkW1lb-Pa4qxsG8sDPVzdotJzjQ4H1tcVX5~JHT0HrVj23sYbJ0dtKy2NTE3UqL8YDldzWHyKKT6KhrQNBZZXAtzUablYA9rOoA2lTb5EDtAqHmdibpgcwdVLWS22Qgc8etLzvHHlrfDrHKVkEQvtMXIUTxkOjXKdIvAtWABHiobuORFTfvqkxIemmC15-RDnTVOX0phCUEG9v59oFg3rTwDiy8YAOppo6Za1o1y~rqSCkQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"O_ct_2_01_5_Partition_function_zeros_for_the_Ising_model_on_complete_graphs_and_on_annealed_scale_free_networks","translated_slug":"","page_count":36,"language":"en","content_type":"Work","owner":{"id":57856370,"first_name":"Ralph","middle_initials":null,"last_name":"Kenna","page_name":"KennaRalph","domain_name":"independent","created_at":"2016-12-09T08:34:18.408-08:00","display_name":"Ralph Kenna","url":"https://independent.academia.edu/KennaRalph"},"attachments":[{"id":85220221,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/85220221/thumbnails/1.jpg","file_name":"1510.pdf","download_url":"https://www.academia.edu/attachments/85220221/download_file?st=MTczMjQ0OTY4Myw4LjIyMi4yMDguMTQ2&st=MTczMjQ0OTY4MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"O_ct_2_01_5_Partition_function_zeros_for.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/85220221/1510-libre.pdf?1651318778=\u0026response-content-disposition=attachment%3B+filename%3DO_ct_2_01_5_Partition_function_zeros_for.pdf\u0026Expires=1732453281\u0026Signature=gKfH-BBoOmkd21et8Ih5RAKJ1yK9A~-4pCyPHgLKaJd6XcCt~xsYEgIM5xVceLzvrkVBQ5hP0IHn2I~h-DZOKTLIQ2UT7RL809dONi0FkW1lb-Pa4qxsG8sDPVzdotJzjQ4H1tcVX5~JHT0HrVj23sYbJ0dtKy2NTE3UqL8YDldzWHyKKT6KhrQNBZZXAtzUablYA9rOoA2lTb5EDtAqHmdibpgcwdVLWS22Qgc8etLzvHHlrfDrHKVkEQvtMXIUTxkOjXKdIvAtWABHiobuORFTfvqkxIemmC15-RDnTVOX0phCUEG9v59oFg3rTwDiy8YAOppo6Za1o1y~rqSCkQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"},{"id":85220222,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/85220222/thumbnails/1.jpg","file_name":"1510.pdf","download_url":"https://www.academia.edu/attachments/85220222/download_file","bulk_download_file_name":"O_ct_2_01_5_Partition_function_zeros_for.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/85220222/1510-libre.pdf?1651318775=\u0026response-content-disposition=attachment%3B+filename%3DO_ct_2_01_5_Partition_function_zeros_for.pdf\u0026Expires=1732453281\u0026Signature=BaxNCdMxFj9V3dR4NgubXVbMlwvA-p8HLXxpBaWz3Hi0A-g~wfqd46UOd3OcbC7a~RAwJjQijXZ3VHjj3jIK4mt6e37mROwyENkiMdrXnrjVgUwG45IaM3cR311Bkym9Agw19nwtqZlBabn7csuT2rsC96tMz83PTMW~MU5z79ECKcNBjGmke0DCvgrUzKNGefTThPFFYtkwhz2QVQYw4QdyQHEksLsh6Kt~egkiugDce7n55ICZius5TITRXhiw--fCM48424G3RK6DNgUOz0ZsqAe~sOJhbFlB0ucLkB-pv7stkePA2Rdsx5frBOTa47v95OSnb-t94ijL50knjA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[],"urls":[{"id":20060977,"url":"http://export.arxiv.org/pdf/1510.00534"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="78033771"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/78033771/The_two_point_resistance_of_fan_networks"><img alt="Research paper thumbnail of The two-point resistance of fan networks" class="work-thumbnail" src="https://attachments.academia-assets.com/85220218/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/78033771/The_two_point_resistance_of_fan_networks">The two-point resistance of fan networks</a></div><div class="wp-workCard_item"><span>arXiv: Statistical Mechanics</span><span>, 2014</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The problem of the two-point resistance in various networks has recently received considerable at...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The problem of the two-point resistance in various networks has recently received considerable attention. Here we consider the problem on a fan-resistor network, which is a segment of the cobweb network. Using a recently developed approach, we obtain the exact resistance between two arbitrary nodes on such a network. As a byproduct, the analysis also delivers the solution of the spanning tree problem on the fan network.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="4a981843ac7a3d8b9265ca1c3a29417b" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":85220218,"asset_id":78033771,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/85220218/download_file?st=MTczMjQ0OTY4Myw4LjIyMi4yMDguMTQ2&st=MTczMjQ0OTY4MSw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="78033771"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="78033771"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 78033771; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=78033771]").text(description); $(".js-view-count[data-work-id=78033771]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 78033771; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='78033771']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 78033771, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "4a981843ac7a3d8b9265ca1c3a29417b" } } $('.js-work-strip[data-work-id=78033771]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":78033771,"title":"The two-point resistance of fan networks","translated_title":"","metadata":{"abstract":"The problem of the two-point resistance in various networks has recently received considerable attention. 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The model is intended for analysis of ordering in systems comprising agents which, although matching in their binarity (i.e., maintaining the iconic Ising features of ‘+’ or ‘−’, ‘up’ or ‘down’, ‘yes’ or ‘no’), differ in their strength. To investigate the interplay between variable properties of nodes and interactions between them, we study the model on a complex network where both the spin strength and degree distributions are governed by power laws. We show that in the annealed network approximation, thermodynamic functions of the model are self-averaging and we obtain an exact solution for the partition function. This allows us derive the leading temperature and field dependencies of thermodynamic functions, their critical behavior, and logarithmic corrections at the interface of different phases. We find the delicate interplay of the two power laws leads to new univers...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="622910e8149f909841c4efdbb1b5592f" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":85220215,"asset_id":78033770,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/85220215/download_file?st=MTczMjQ0OTY4Myw4LjIyMi4yMDguMTQ2&st=MTczMjQ0OTY4Miw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="78033770"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="78033770"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 78033770; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=78033770]").text(description); $(".js-view-count[data-work-id=78033770]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 78033770; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='78033770']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 78033770, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "622910e8149f909841c4efdbb1b5592f" } } $('.js-work-strip[data-work-id=78033770]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":78033770,"title":"Generalized Ising Model on a Scale-Free Network: An Interplay of Power Laws","translated_title":"","metadata":{"abstract":"We consider a recently introduced generalization of the Ising model in which individual spin strength can vary. The model is intended for analysis of ordering in systems comprising agents which, although matching in their binarity (i.e., maintaining the iconic Ising features of ‘+’ or ‘−’, ‘up’ or ‘down’, ‘yes’ or ‘no’), differ in their strength. To investigate the interplay between variable properties of nodes and interactions between them, we study the model on a complex network where both the spin strength and degree distributions are governed by power laws. We show that in the annealed network approximation, thermodynamic functions of the model are self-averaging and we obtain an exact solution for the partition function. This allows us derive the leading temperature and field dependencies of thermodynamic functions, their critical behavior, and logarithmic corrections at the interface of different phases. 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This allows us derive the leading temperature and field dependencies of thermodynamic functions, their critical behavior, and logarithmic corrections at the interface of different phases. 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="78033769"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/78033769/Narrative_structure_ofA_Song_of_Ice_and_Firecreates_a_fictional_world_with_realistic_measures_of_social_complexity"><img alt="Research paper thumbnail of Narrative structure ofA Song of Ice and Firecreates a fictional world with realistic measures of social complexity" class="work-thumbnail" src="https://attachments.academia-assets.com/85220363/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/78033769/Narrative_structure_ofA_Song_of_Ice_and_Firecreates_a_fictional_world_with_realistic_measures_of_social_complexity">Narrative structure ofA Song of Ice and Firecreates a fictional world with realistic measures of social complexity</a></div><div class="wp-workCard_item"><span>Proceedings of the National Academy of Sciences</span><span>, 2020</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Network science and data analytics are used to quantify static and dynamic structures in George R...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Network science and data analytics are used to quantify static and dynamic structures in George R. R. Martin’s epic novels,A Song of Ice and Fire, works noted for their scale and complexity. By tracking the network of character interactions as the story unfolds, it is found that structural properties remain approximately stable and comparable to real-world social networks. Furthermore, the degrees of the most connected characters reflect a cognitive limit on the number of concurrent social connections that humans tend to maintain. We also analyze the distribution of time intervals between significant deaths measured with respect to the in-story timeline. These are consistent with power-law distributions commonly found in interevent times for a range of nonviolent human activities in the real world. We propose that structural features in the narrative that are reflected in our actual social world help readers to follow and to relate to the story, despite its sprawling extent. It is a...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="8e27c96928e6839d5321cc784b14937b" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":85220363,"asset_id":78033769,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/85220363/download_file?st=MTczMjQ0OTY4Myw4LjIyMi4yMDguMTQ2&st=MTczMjQ0OTY4Miw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="78033769"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="78033769"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 78033769; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=78033769]").text(description); $(".js-view-count[data-work-id=78033769]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 78033769; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='78033769']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 78033769, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "8e27c96928e6839d5321cc784b14937b" } } $('.js-work-strip[data-work-id=78033769]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":78033769,"title":"Narrative structure ofA Song of Ice and Firecreates a fictional world with realistic measures of social complexity","translated_title":"","metadata":{"abstract":"Network science and data analytics are used to quantify static and dynamic structures in George R. 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These are consistent with power-law distributions commonly found in interevent times for a range of nonviolent human activities in the real world. We propose that structural features in the narrative that are reflected in our actual social world help readers to follow and to relate to the story, despite its sprawling extent. 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="78033768"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/78033768/Use_of_the_Complex_Zeros_of_the_Partition_Function_to_Investigate_the_Critical_Behavior_of_the_Generalized_Interacting_Self_Avoiding_Trail_Model"><img alt="Research paper thumbnail of Use of the Complex Zeros of the Partition Function to Investigate the Critical Behavior of the Generalized Interacting Self-Avoiding Trail Model" class="work-thumbnail" src="https://attachments.academia-assets.com/85220212/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/78033768/Use_of_the_Complex_Zeros_of_the_Partition_Function_to_Investigate_the_Critical_Behavior_of_the_Generalized_Interacting_Self_Avoiding_Trail_Model">Use of the Complex Zeros of the Partition Function to Investigate the Critical Behavior of the Generalized Interacting Self-Avoiding Trail Model</a></div><div class="wp-workCard_item"><span>Entropy</span><span>, 2019</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The complex zeros of the canonical (fixed walk-length) partition function are calculated for both...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The complex zeros of the canonical (fixed walk-length) partition function are calculated for both the self-avoiding trails model and the vertex-interacting self-avoiding walk model, both in bulk and in the presence of an attractive surface. The finite-size behavior of the zeros is used to estimate the location of phase transitions: the collapse transition in the bulk and the adsorption transition in the presence of a surface. The bulk and surface cross-over exponents, ϕ and ϕ S , are estimated from the scaling behavior of the leading partition function zeros.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="bcda17b77e015702b545d10c177f4612" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":85220212,"asset_id":78033768,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/85220212/download_file?st=MTczMjQ0OTY4Myw4LjIyMi4yMDguMTQ2&st=MTczMjQ0OTY4Miw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="78033768"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="78033768"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 78033768; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=78033768]").text(description); $(".js-view-count[data-work-id=78033768]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 78033768; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='78033768']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 78033768, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "bcda17b77e015702b545d10c177f4612" } } $('.js-work-strip[data-work-id=78033768]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":78033768,"title":"Use of the Complex Zeros of the Partition Function to Investigate the Critical Behavior of the Generalized Interacting Self-Avoiding Trail Model","translated_title":"","metadata":{"abstract":"The complex zeros of the canonical (fixed walk-length) partition function are calculated for both the self-avoiding trails model and the vertex-interacting self-avoiding walk model, both in bulk and in the presence of an attractive surface. 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The bulk and surface cross-over exponents, ϕ and ϕ S , are estimated from the scaling behavior of the leading partition function zeros.","internal_url":"https://www.academia.edu/78033768/Use_of_the_Complex_Zeros_of_the_Partition_Function_to_Investigate_the_Critical_Behavior_of_the_Generalized_Interacting_Self_Avoiding_Trail_Model","translated_internal_url":"","created_at":"2022-04-30T04:19:25.595-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":57856370,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":85220212,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/85220212/thumbnails/1.jpg","file_name":"pdf.pdf","download_url":"https://www.academia.edu/attachments/85220212/download_file?st=MTczMjQ0OTY4Myw4LjIyMi4yMDguMTQ2&st=MTczMjQ0OTY4Miw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Use_of_the_Complex_Zeros_of_the_Partitio.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/85220212/pdf-libre.pdf?1651318771=\u0026response-content-disposition=attachment%3B+filename%3DUse_of_the_Complex_Zeros_of_the_Partitio.pdf\u0026Expires=1732453282\u0026Signature=M9dANs7yB5D6F4LYU2BPVAzP7sdNlYyGAYDXh3mZe1Z86vpoESz8lPK3LCDUuKHix-QcUXohWzM8fCgeU~AI1WydDSN7keYCohiTfA~4HMzx7mgBc-ieqWxmSCH3T4~zkRsPEX8ZNq6lvvxQQQ0WIu3bqTd4n3a40NlRpmZCWGB0bW4xidJ7yAKQwABdyxqIJNOF0IxkiH9eOR2YMy9XasHLpIzBRaPNktN9mzwDSTbRSNkI3~Ec~hsFjEgHDC5qbbxMsOMIknEdWOfD8O910XmKoWYlrPb~kLguvJCTofFZs1ByLJWjNzqnDmAG5zCvGaUBK4vxQ3mzRZ9pJXsjyA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Use_of_the_Complex_Zeros_of_the_Partition_Function_to_Investigate_the_Critical_Behavior_of_the_Generalized_Interacting_Self_Avoiding_Trail_Model","translated_slug":"","page_count":14,"language":"en","content_type":"Work","owner":{"id":57856370,"first_name":"Ralph","middle_initials":null,"last_name":"Kenna","page_name":"KennaRalph","domain_name":"independent","created_at":"2016-12-09T08:34:18.408-08:00","display_name":"Ralph Kenna","url":"https://independent.academia.edu/KennaRalph"},"attachments":[{"id":85220212,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/85220212/thumbnails/1.jpg","file_name":"pdf.pdf","download_url":"https://www.academia.edu/attachments/85220212/download_file?st=MTczMjQ0OTY4Myw4LjIyMi4yMDguMTQ2&st=MTczMjQ0OTY4Miw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Use_of_the_Complex_Zeros_of_the_Partitio.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/85220212/pdf-libre.pdf?1651318771=\u0026response-content-disposition=attachment%3B+filename%3DUse_of_the_Complex_Zeros_of_the_Partitio.pdf\u0026Expires=1732453282\u0026Signature=M9dANs7yB5D6F4LYU2BPVAzP7sdNlYyGAYDXh3mZe1Z86vpoESz8lPK3LCDUuKHix-QcUXohWzM8fCgeU~AI1WydDSN7keYCohiTfA~4HMzx7mgBc-ieqWxmSCH3T4~zkRsPEX8ZNq6lvvxQQQ0WIu3bqTd4n3a40NlRpmZCWGB0bW4xidJ7yAKQwABdyxqIJNOF0IxkiH9eOR2YMy9XasHLpIzBRaPNktN9mzwDSTbRSNkI3~Ec~hsFjEgHDC5qbbxMsOMIknEdWOfD8O910XmKoWYlrPb~kLguvJCTofFZs1ByLJWjNzqnDmAG5zCvGaUBK4vxQ3mzRZ9pJXsjyA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"},{"id":85220213,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/85220213/thumbnails/1.jpg","file_name":"pdf.pdf","download_url":"https://www.academia.edu/attachments/85220213/download_file","bulk_download_file_name":"Use_of_the_Complex_Zeros_of_the_Partitio.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/85220213/pdf-libre.pdf?1651318774=\u0026response-content-disposition=attachment%3B+filename%3DUse_of_the_Complex_Zeros_of_the_Partitio.pdf\u0026Expires=1732453282\u0026Signature=bUDQbL0hXFtDIhulYs6pzBPEYz8e2A92dUnb7KcpffdtAaRjTxa4jMNeFsGTH-NfOG4e-t71kpuZhCSt6G-7mGj6L4NzL7dDKV7O63x9bPy2fhGG3FS31jqvPGX8ozgwDt3IccVzwYDrmRBMa-DCfLvR-fEPD73~VozwGscV-6H9DbQc1-OjmYG1DRpqsTBLUNd2m2DxVA9bdr0wbtrHmAdJLAgtrXV5DUodSX5W~li6vpnGwO2xAz3mu14aEVPma36HfZBWr8sVslD0rwnd-18MbXKR4cdiCHxtqRAsrTobsLrT2ropT5i45njGCatBJRM6SdBF4Oh534mzDrqIQA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":36265,"name":"Entropy","url":"https://www.academia.edu/Documents/in/Entropy"},{"id":80414,"name":"Mathematical Sciences","url":"https://www.academia.edu/Documents/in/Mathematical_Sciences"},{"id":118582,"name":"Physical sciences","url":"https://www.academia.edu/Documents/in/Physical_sciences"}],"urls":[{"id":20060973,"url":"http://www.mdpi.com/1099-4300/21/2/153/pdf"}]}, dispatcherData: dispatcherData }); 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dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "46ccf6bcd5382d677815f1d988d5ec68" } } $('.js-work-strip[data-work-id=78033767]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":78033767,"title":"Universal finite-size scaling for percolation theory in high dimensions","translated_title":"","metadata":{"publisher":"IOP Publishing","grobid_abstract":"We present a unifying, consistent, finite-size-scaling picture for percolation theory bringing it into the framework of a general, renormalization-group-based, scaling scheme for systems above their upper critical dimensions d c. Behaviour at the critical point is non-universal in d \u003e d c = 6 dimensions. Proliferation of the largest clusters, with fractal dimension 4, is associated with the breakdown of hyperscaling there when free boundary conditions are used. But when the boundary conditions are periodic, the maximal clusters have dimension D = 2d/3, and obey random-graph asymptotics. Universality is instead manifest at the pseudocritical point, where the failure of hyperscaling in its traditional form is universally associated with random-graph-type asymptotics for critical cluster sizes, independent of boundary conditions.","publication_date":{"day":null,"month":null,"year":2017,"errors":{}},"publication_name":"Journal of Physics A: Mathematical and Theoretical","grobid_abstract_attachment_id":85220366},"translated_abstract":null,"internal_url":"https://www.academia.edu/78033767/Universal_finite_size_scaling_for_percolation_theory_in_high_dimensions","translated_internal_url":"","created_at":"2022-04-30T04:19:25.378-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":57856370,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":85220366,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/85220366/thumbnails/1.jpg","file_name":"1606.00315.pdf","download_url":"https://www.academia.edu/attachments/85220366/download_file?st=MTczMjQ0OTY4Myw4LjIyMi4yMDguMTQ2&st=MTczMjQ0OTY4Miw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Universal_finite_size_scaling_for_percol.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/85220366/1606.00315-libre.pdf?1651318767=\u0026response-content-disposition=attachment%3B+filename%3DUniversal_finite_size_scaling_for_percol.pdf\u0026Expires=1732453282\u0026Signature=BtbFZRq4RekZ42DSwXwUDW0tjT3Kn0-I3YRyznKFfQ5LQc6-kK0Ep0gBP8ZvqqsU5XEtuWOernw8U6KK4WpWMDpT0iIBRD4SibaaQ710hain8YSybBKxT4OOiSG3vXmfxUNQppC4s0eZiOotP8FOuS5GEaUK6QA4qGIJybHp6h5ZIk78IGYvA6Fdvk2mG7FrvraD1SW26R5JtuvGxC-HJryOSMD4kwHACPZ2fKiu6ugxNbqOKaUrlVPMDQchLvLYGz1DsuwELzHA62N-bp5iZi6iBYqJxUgyntsF8WdUHQuJnHsLOmvoYm-Jj0Nu9oJJTYQZbgaPQ6oQ~GkNEzh-Hg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Universal_finite_size_scaling_for_percolation_theory_in_high_dimensions","translated_slug":"","page_count":27,"language":"en","content_type":"Work","owner":{"id":57856370,"first_name":"Ralph","middle_initials":null,"last_name":"Kenna","page_name":"KennaRalph","domain_name":"independent","created_at":"2016-12-09T08:34:18.408-08:00","display_name":"Ralph Kenna","url":"https://independent.academia.edu/KennaRalph"},"attachments":[{"id":85220366,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/85220366/thumbnails/1.jpg","file_name":"1606.00315.pdf","download_url":"https://www.academia.edu/attachments/85220366/download_file?st=MTczMjQ0OTY4Myw4LjIyMi4yMDguMTQ2&st=MTczMjQ0OTY4Miw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Universal_finite_size_scaling_for_percol.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/85220366/1606.00315-libre.pdf?1651318767=\u0026response-content-disposition=attachment%3B+filename%3DUniversal_finite_size_scaling_for_percol.pdf\u0026Expires=1732453282\u0026Signature=BtbFZRq4RekZ42DSwXwUDW0tjT3Kn0-I3YRyznKFfQ5LQc6-kK0Ep0gBP8ZvqqsU5XEtuWOernw8U6KK4WpWMDpT0iIBRD4SibaaQ710hain8YSybBKxT4OOiSG3vXmfxUNQppC4s0eZiOotP8FOuS5GEaUK6QA4qGIJybHp6h5ZIk78IGYvA6Fdvk2mG7FrvraD1SW26R5JtuvGxC-HJryOSMD4kwHACPZ2fKiu6ugxNbqOKaUrlVPMDQchLvLYGz1DsuwELzHA62N-bp5iZi6iBYqJxUgyntsF8WdUHQuJnHsLOmvoYm-Jj0Nu9oJJTYQZbgaPQ6oQ~GkNEzh-Hg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":498,"name":"Physics","url":"https://www.academia.edu/Documents/in/Physics"},{"id":80414,"name":"Mathematical Sciences","url":"https://www.academia.edu/Documents/in/Mathematical_Sciences"},{"id":118582,"name":"Physical sciences","url":"https://www.academia.edu/Documents/in/Physical_sciences"}],"urls":[{"id":20060972,"url":"http://stacks.iop.org/1751-8121/50/i=23/a=235001/pdf"}]}, dispatcherData: dispatcherData }); 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In particular, two types of method have emerged. One is based on potentials and the evaluation of eigenvalues and eigenvectors of the Laplacian matrix associated with the network or its minors. The second method is based on a recurrence relation associated with the distribution of currents in the network. 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