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[{"id":32578334,"identifier":"Attachment_32578334","shouldShowBulkDownload":false}]; window.loswp.shouldDetectTimezone = true; window.loswp.shouldShowBulkDownload = true; window.loswp.showSignupCaptcha = false window.loswp.willEdgeCache = false; window.loswp.work = {"work":{"id":5458711,"created_at":"2013-12-17T06:13:28.201-08:00","from_world_paper_id":null,"updated_at":"2024-11-16T23:00:59.847-08:00","_data":{"grobid_abstract":"An exact enumeration approach is developed for the backbone fractal of the incipient infinite cluster at the percolation threshold. We use this approach to calculate exactly the first low-density expansion of LBB@) for arbitrary system dimensionality d, where L B B @ ) is the mean number of backbone bonds and p is the bond occupation probability. Standard series extrapolation methods provide estimates of the fractal dimension of the backbone for all d ; these disagree with the Sierpinski gasket model of the backbone. We also calculate the first low-density expansions of Lmin@) and L e d @ ) which are, respectively, the mean number of bonds in the minimum path between i and","grobid_abstract_attachment_id":"32578334"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"Exact enumeration approach to fractal properties of the percolation backbone and 1/σ expansion","broadcastable":true,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [7630487]; window.loswp.locale = "en"; window.loswp.countryCode = "SG"; window.loswp.cwvAbTestBucket = ""; window.loswp.designVariant = "ds_vanilla"; window.loswp.fullPageMobileSutdModalVariant = "control"; window.loswp.useOptimizedScribd4genScript = false; window.loswp.appleClientId = 'edu.academia.applesignon';</script><script defer="" src="https://accounts.google.com/gsi/client"></script><div class="ds-loswp-container"><div class="ds-work-card--grid-container"><div class="ds-work-card--container js-loswp-work-card"><div class="ds-work-card--cover"><div class="ds-work-cover--wrapper"><div class="ds-work-cover--container"><button class="ds-work-cover--clickable js-swp-download-button" data-signup-modal="{"location":"swp-splash-paper-cover","attachmentId":32578334,"attachmentType":"pdf"}"><img alt="First page of “Exact enumeration approach to fractal properties of the percolation backbone and 1/σ expansion”" class="ds-work-cover--cover-thumbnail" src="https://0.academia-photos.com/attachment_thumbnails/32578334/mini_magick20190415-31707-1h91mq1.png?1555383589" /><img alt="PDF Icon" class="ds-work-cover--file-icon" src="//a.academia-assets.com/assets/single_work_splash/adobe.icon-574afd46eb6b03a77a153a647fb47e30546f9215c0ee6a25df597a779717f9ef.svg" /><div class="ds-work-cover--hover-container"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span><p>Download Free PDF</p></div><div class="ds-work-cover--ribbon-container">Download Free PDF</div><div class="ds-work-cover--ribbon-triangle"></div></button></div></div></div><div class="ds-work-card--work-information"><h1 class="ds-work-card--work-title">Exact enumeration approach to fractal properties of the percolation backbone and 1/σ expansion</h1><div class="ds-work-card--work-authors ds-work-card--detail"><a class="ds-work-card--author js-wsj-grid-card-author ds2-5-body-md ds2-5-body-link" data-author-id="7630487" href="https://bu.academia.edu/EugeneStanley"><img alt="Profile image of Eugene Stanley" class="ds-work-card--author-avatar" src="https://0.academia-photos.com/7630487/2749271/3203685/s65_eugene.stanley.jpg" />Eugene Stanley</a></div><div class="ds-work-card--button-container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--work-card","attachmentId":32578334,"attachmentType":"pdf","workUrl":"https://www.academia.edu/5458711/Exact_enumeration_approach_to_fractal_properties_of_the_percolation_backbone_and_1_%CF%83_expansion"}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--work-card","attachmentId":32578334,"attachmentType":"pdf","workUrl":"https://www.academia.edu/5458711/Exact_enumeration_approach_to_fractal_properties_of_the_percolation_backbone_and_1_%CF%83_expansion"}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div></div><div data-auto_select="false" data-client_id="331998490334-rsn3chp12mbkiqhl6e7lu2q0mlbu0f1b" data-doc_id="32578334" data-landing_url="https://www.academia.edu/5458711/Exact_enumeration_approach_to_fractal_properties_of_the_percolation_backbone_and_1_%CF%83_expansion" data-login_uri="https://www.academia.edu/registrations/google_one_tap" data-moment_callback="onGoogleOneTapEvent" id="g_id_onload"></div><div class="ds-top-related-works--grid-container"><div class="ds-related-content--container ds-top-related-works--container"><h2 class="ds-related-content--heading">Related papers</h2><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="0" data-entity-id="89896103" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/89896103/Physical_Properties_of_a_New_Fractal_Model_of_Percolation_Clusters">Physical Properties of a New Fractal Model of Percolation Clusters</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="31313596" href="https://independent.academia.edu/AAharony">A. 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