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window.loswp.showSignupCaptcha = false window.loswp.willEdgeCache = false; window.loswp.work = {"work":{"id":105366172,"created_at":"2023-08-07T18:52:54.890-07:00","from_world_paper_id":238463941,"updated_at":"2024-11-26T02:00:53.990-08:00","_data":{"grobid_abstract":"In the past few years, several studies have explored the topology of interactions in different complex systems. Areas of investigation span from biology to engineering, physics and the social sciences. Although having different microscopic dynamics, the results demonstrate that most systems under consideration tend to self-organize into structures that share common features. In particular, the networks of interaction are characterized by a power law distribution, P (k) ∼ k −α , in the number of connections per node, k, over several orders of magnitude. Networks that fulfill this propriety of scale-invariance are referred to as \"scale-free\". In the present work we explore the implication of scale-free topologies in the antiferromagnetic (AF) Ising model and in a stochastic model of opinion formation. In the first case we show that the implicit disorder and frustration lead to a spinglass phase transition not observed for the AF Ising model on standard lattices. We further illustrate that the opinion formation model produces a coherent, turbulent-like dynamics for a certain range of parameters. The influence, of random or targeted exclusion of nodes is studied.","publication_date":"2006,,","publication_name":"Proceedings of SPIE - The International Society for Optical Engineering","grobid_abstract_attachment_id":"104839598"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"Scale-free networks in complex systems","broadcastable":false,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [30664615]; window.loswp.locale = "en"; window.loswp.countryCode = "SG"; window.loswp.cwvAbTestBucket = ""; window.loswp.designVariant = "ds_vanilla"; window.loswp.fullPageMobileSutdModalVariant = "full_page_mobile_sutd_modal"; window.loswp.useOptimizedScribd4genScript = false; window.loginModal = {}; window.loginModal.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":104839598,"attachmentType":"pdf"}"><img alt="First page of “Scale-free networks in complex systems”" class="ds-work-cover--cover-thumbnail" src="https://0.academia-photos.com/attachment_thumbnails/104839598/mini_magick20230808-1-68c5vr.png?1691460221" /><img alt="PDF Icon" class="ds-work-cover--file-icon" src="//a.academia-assets.com/images/single_work_splash/adobe_icon.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">Scale-free networks in complex systems</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="30664615" href="https://adelaide.academia.edu/AnthonyWilliams"><img alt="Profile image of Anthony G Williams" class="ds-work-card--author-avatar" src="//a.academia-assets.com/images/s65_no_pic.png" />Anthony G Williams</a></div><div class="ds-work-card--detail"><p class="ds-work-card--detail ds2-5-body-sm">2006, Proceedings of SPIE - The International Society for Optical Engineering</p><div class="ds-work-card--work-metadata"><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">visibility</span><p class="ds2-5-body-sm" id="work-metadata-view-count">…</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">description</span><p class="ds2-5-body-sm">9 pages</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">link</span><p class="ds2-5-body-sm">1 file</p></div></div><script>(async () => { const workId = 105366172; 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if (!viewCountBody) { throw new Error('Failed to find work views element'); } viewCountBody.textContent = `${commaizedViewCount} views`; } catch (error) { // Remove the whole views element if there was some issue parsing. document.getElementById('work-metadata-view-count')?.parentNode?.remove(); throw new Error(`Failed to parse view count: ${viewCount}`, error); } }; // If the DOM is still loading, wait for it to be ready before updating the view count. if (document.readyState === "loading") { document.addEventListener('DOMContentLoaded', () => { updateViewCount(viewCount); }); // Otherwise, just update it immediately. } else { updateViewCount(viewCount); } })();</script></div><p class="ds-work-card--work-abstract ds-work-card--detail ds2-5-body-md">In the past few years, several studies have explored the topology of interactions in different complex systems. Areas of investigation span from biology to engineering, physics and the social sciences. Although having different microscopic dynamics, the results demonstrate that most systems under consideration tend to self-organize into structures that share common features. In particular, the networks of interaction are characterized by a power law distribution, P (k) ∼ k −α , in the number of connections per node, k, over several orders of magnitude. Networks that fulfill this propriety of scale-invariance are referred to as "scale-free". In the present work we explore the implication of scale-free topologies in the antiferromagnetic (AF) Ising model and in a stochastic model of opinion formation. In the first case we show that the implicit disorder and frustration lead to a spinglass phase transition not observed for the AF Ising model on standard lattices. We further illustrate that the opinion formation model produces a coherent, turbulent-like dynamics for a certain range of parameters. The influence, of random or targeted exclusion of nodes is studied.</p><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":104839598,"attachmentType":"pdf","workUrl":"https://www.academia.edu/105366172/Scale_free_networks_in_complex_systems"}">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":104839598,"attachmentType":"pdf","workUrl":"https://www.academia.edu/105366172/Scale_free_networks_in_complex_systems"}"><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="104839598" data-landing_url="https://www.academia.edu/105366172/Scale_free_networks_in_complex_systems" 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="78033770" 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/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 class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="57856370" href="https://independent.academia.edu/KennaRalph">Ralph Kenna</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Entropy, 2021</p><p class="ds-related-work--abstract ds2-5-body-sm">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...</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Generalized Ising Model on a Scale-Free Network: An Interplay of Power Laws","attachmentId":85220215,"attachmentType":"pdf","work_url":"https://www.academia.edu/78033770/Generalized_Ising_Model_on_a_Scale_Free_Network_An_Interplay_of_Power_Laws","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/78033770/Generalized_Ising_Model_on_a_Scale_Free_Network_An_Interplay_of_Power_Laws"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="1" data-entity-id="17494383" 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/17494383/Irreversible_opinion_spreading_on_scale_free_networks">Irreversible opinion spreading on scale-free networks</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="37143984" href="https://nih.academia.edu/Juli%C3%A1nCandia">Julián Candia</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical Review E, 2007</p><p class="ds-related-work--abstract ds2-5-body-sm">We study the dynamical and critical behavior of a model for irreversible opinion spreading on Barabási-Albert (BA) scale-free networks by performing extensive Monte Carlo simulations. The opinion spreading within an inhomogeneous society is investigated by means of the magnetic Eden model, a nonequilibrium kinetic model for the growth of binary mixtures in contact with a thermal bath. The deposition dynamics, which is studied as a function of the degree of the occupied sites, shows evidence for the leading role played by hubs in the growth process. Systems of finite size grow either ordered or disordered, depending on the temperature. By means of standard finite-size scaling procedures, the effective order-disorder phase transitions are found to persist in the thermodynamic limit. This critical behavior, however, is absent in related equilibrium spin systems such as the Ising model on BA scale-free networks, which in the thermodynamic limit only displays a ferromagnetic phase. The dependence of these results on the degree exponent is also discussed for the case of uncorrelated scale-free networks.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Irreversible opinion spreading on scale-free networks","attachmentId":39541500,"attachmentType":"pdf","work_url":"https://www.academia.edu/17494383/Irreversible_opinion_spreading_on_scale_free_networks","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/17494383/Irreversible_opinion_spreading_on_scale_free_networks"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="2" data-entity-id="17494382" 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/17494382/Non_equilibrium_opinion_spreading_on_2D_small_world_networks">Non-equilibrium opinion spreading on 2D small-world networks</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="37143984" href="https://nih.academia.edu/Juli%C3%A1nCandia">Julián Candia</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Statistical Mechanics: Theory and Experiment, 2007</p><p class="ds-related-work--abstract ds2-5-body-sm">Irreversible opinion spreading phenomena are studied on small-world networks generated from 2D regular lattices by means of the magnetic Eden model, a nonequilibrium kinetic model for the growth of binary mixtures in contact with a thermal bath. In this model, the opinion or decision of an individual is affected by those of their acquaintances, but opinion changes (analogous to spin flips in an Ising-like model) are not allowed. Particularly, we focus on aspects inherent to the underlying 2D nature of the substrate, such as domain growth and cluster size distributions. Larger shortcut fractions are observed to favor long-range ordering connections between distant clusters across the network, while the temperature is shown to drive the system across an order-disorder transition, in agreement with previous investigations on related equilibrium spin systems. Furthermore, the extrapolated phase diagram, as well as the correlation length critical exponent, are determined by means of standard finite-size scaling procedures.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Non-equilibrium opinion spreading on 2D small-world networks","attachmentId":39541499,"attachmentType":"pdf","work_url":"https://www.academia.edu/17494382/Non_equilibrium_opinion_spreading_on_2D_small_world_networks","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/17494382/Non_equilibrium_opinion_spreading_on_2D_small_world_networks"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="3" data-entity-id="18707822" 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/18707822/Topological_phase_transitions_of_random_networks">Topological phase transitions of random networks</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="38775154" href="https://elte-hu.academia.edu/Tam%C3%A1sVicsek">Tamás Vicsek</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physica A: Statistical Mechanics and its Applications, 2004</p><p class="ds-related-work--abstract ds2-5-body-sm">To provide a phenomenological theory for the various interesting transitions in restructuring networks we employ a statistical mechanical approach with detailed balance satisÿed for the transitions between topological states. This enables us to establish an equivalence between the equilibrium rewiring problem we consider and the dynamics of a lattice gas on the edge-dual graph of a fully connected network. By assigning energies to the di erent network topologies and deÿning the appropriate order parameters, we ÿnd a rich variety of topological phase transitions, deÿned as singular changes in the essential feature(s) of the global connectivity as a function of a parameter playing the role of the temperature. In the "critical point" scale-free networks can be recovered.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Topological phase transitions of random networks","attachmentId":40211672,"attachmentType":"pdf","work_url":"https://www.academia.edu/18707822/Topological_phase_transitions_of_random_networks","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/18707822/Topological_phase_transitions_of_random_networks"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="4" data-entity-id="31996754" 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/31996754/Nonequilibrium_Phase_Transitions_in_Directed_Small_World_Networks">Nonequilibrium Phase Transitions in Directed Small-World Networks</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="40034332" href="https://independent.academia.edu/MiguelRodr%C3%ADguez42">Miguel Rodríguez</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical Review Letters, 2002</p><p class="ds-related-work--abstract ds2-5-body-sm">Many social, biological, and economic systems can be approached by complex networks of interacting units. The behaviour of several models on small-world networks has recently been studied. These models are expected to capture the essential features of the complex processes taking place on real networks like disease spreading, formation of public opinion, distribution of wealth, etc. In many of these systems relations are directed, in the sense that links only act in one direction (outwards or inwards). We investigate the effect of directed links on the behaviour of a simple spin-like model evolving on a small-world network. We show that directed networks may lead to a highly nontrivial phase diagram including first and second-order phase transitions out of equilibrium. 89.75.Hc, 64.60.Ht, 05.70.Fh, 05.70.Ln</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Nonequilibrium Phase Transitions in Directed Small-World Networks","attachmentId":52265598,"attachmentType":"pdf","work_url":"https://www.academia.edu/31996754/Nonequilibrium_Phase_Transitions_in_Directed_Small_World_Networks","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/31996754/Nonequilibrium_Phase_Transitions_in_Directed_Small_World_Networks"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="5" data-entity-id="10828966" 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/10828966/Nonequilibrium_transitions_in_complex_networks_A_model_of_social_interaction">Nonequilibrium transitions in complex networks: A model of social interaction</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="26324295" href="https://uib-es.academia.edu/RToral">Raul Toral</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical Review E, 2003</p><p class="ds-related-work--abstract ds2-5-body-sm">We analyze the non-equilibrium order-disorder transition of Axelrod's model of social interaction in several complex networks. In a small world network, we find a transition between an ordered homogeneous state and a disordered state. The transition point is shifted by the degree of spatial disorder of the underlying network, the network disorder favoring ordered configurations. In random scale-free networks the transition is only observed for finite size systems, showing system size scaling, while in the thermodynamic limit only ordered configurations are always obtained. Thus in the thermodynamic limit the transition disappears. However, in structured scale-free networks, the phase transition between an ordered and a disordered phase is restored.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Nonequilibrium transitions in complex networks: A model of social interaction","attachmentId":47093318,"attachmentType":"pdf","work_url":"https://www.academia.edu/10828966/Nonequilibrium_transitions_in_complex_networks_A_model_of_social_interaction","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/10828966/Nonequilibrium_transitions_in_complex_networks_A_model_of_social_interaction"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="6" data-entity-id="16566750" 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/16566750/Scale_freeness_for_networks_as_a_degenerate_ground_state_A_Hamiltonian_formulation">Scale-freeness for networks as a degenerate ground state: A Hamiltonian formulation</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="35870771" href="https://umu.academia.edu/PetterMinnhagen">Petter Minnhagen</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Europhysics Letters (EPL), 2007</p><p class="ds-related-work--abstract ds2-5-body-sm">Complex systems PACS 89.75.Fb -Structures and organization in complex systems PACS 89.75.Hc -Networks and genealogical trees PACS 64.60.Cn -Order-disorder transformations; statistical mechanics of model systems</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Scale-freeness for networks as a degenerate ground state: A Hamiltonian formulation","attachmentId":42435687,"attachmentType":"pdf","work_url":"https://www.academia.edu/16566750/Scale_freeness_for_networks_as_a_degenerate_ground_state_A_Hamiltonian_formulation","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/16566750/Scale_freeness_for_networks_as_a_degenerate_ground_state_A_Hamiltonian_formulation"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="7" data-entity-id="25284702" 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/25284702/Trading_Interactions_for_Topology_in_Scale_Free_Networks">Trading Interactions for Topology in Scale-Free Networks</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="48650394" href="https://independent.academia.edu/JIndekeu">J. Indekeu</a><span>, </span><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="48662959" href="https://independent.academia.edu/CVanderzande">C. Vanderzande</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical Review Letters, 2005</p><p class="ds-related-work--abstract ds2-5-body-sm">Scale-free networks with topology-dependent interactions are studied. It is shown that the universality classes of critical behavior, which conventionally depend only on topology, can also be explored by tuning the interactions. A mapping, γ ′ = (γ − µ)/(1 − µ), describes how a shift of the standard exponent γ of the degree distribution P (q) can absorb the effect of degree-dependent pair interactions Jij ∝ (qiqj ) −µ . Replica technique, cavity method and Monte Carlo simulation support the physical picture suggested by Landau theory for the critical exponents and by the Bethe-Peierls approximation for the critical temperature. The equivalence of topology and interaction holds for equilibrium and non-equilibrium systems, and is illustrated with interdisciplinary applications.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Trading Interactions for Topology in Scale-Free Networks","attachmentId":45585872,"attachmentType":"pdf","work_url":"https://www.academia.edu/25284702/Trading_Interactions_for_Topology_in_Scale_Free_Networks","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/25284702/Trading_Interactions_for_Topology_in_Scale_Free_Networks"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="8" data-entity-id="97416680" 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/97416680/Network_complexity_and_topological_phase_transitions">Network complexity and topological phase transitions</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="8302726" href="https://independent.academia.edu/MiguelKiwi">Miguel Kiwi</a></div><p class="ds-related-work--metadata ds2-5-body-xs">arXiv: Statistical Mechanics, 2015</p><p class="ds-related-work--abstract ds2-5-body-sm">A new type of collective excitations, due exclusively to the topology of a complex random network that can be characterized by a fractal dimension $D_F$, is investigated. We show analytically that these excitations generate phase transitions due to the non-periodic topology of the $D_F&gt;1$ complex network. An Ising system, with long range interactions over such a network, is studied in detail to support the claim. The analytic treatment is possible because the evaluation of the partition function can be decomposed into closed factor loops, in spite of the architectural complexity. This way we compute the magnetization distribution, magnetization loops, and the two point correlation function; and relate them to the network topology. In summary, the removal of the infrared divergences leads to an unconventional phase transition, where spin correlations are robust against thermal fluctuations.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Network complexity and topological phase transitions","attachmentId":99044513,"attachmentType":"pdf","work_url":"https://www.academia.edu/97416680/Network_complexity_and_topological_phase_transitions","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/97416680/Network_complexity_and_topological_phase_transitions"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="9" data-entity-id="20594517" 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/20594517/Non_equilibrium_phase_transitions_of_the_Ising_model_on_networks">Non equilibrium phase transitions of the Ising model on networks</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="19572780" href="https://caluniv.academia.edu/ParongamaSen">Parongama Sen</a></div><p class="ds-related-work--abstract ds2-5-body-sm">A zero temperature quench of the Ising model is known to lead to a frozen steady state on random and small world networks. We study such quenches on random scale free networks (RSF) and compare the scenario with that in the Barab\&#39;{a}si-Albert network (BA) and the Watts Strogatz (WS) addition type network. While frozen states are present in all the cases, the RSF shows an order-disorder phase transition of mean field nature as in the WS model as well as the existence of two absorbing phases separated by an active phase. The WS network also shows an active-absorbing (A-A) phase transition occurring at the known order-disorder transition point. The comparison of the RSF and the BA network results show interesting difference in finite size dependence.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Non equilibrium phase transitions of the Ising model on networks","attachmentId":41455793,"attachmentType":"pdf","work_url":"https://www.academia.edu/20594517/Non_equilibrium_phase_transitions_of_the_Ising_model_on_networks","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/20594517/Non_equilibrium_phase_transitions_of_the_Ising_model_on_networks"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div></div></div><div class="ds-sticky-ctas--wrapper js-loswp-sticky-ctas hidden"><div class="ds-sticky-ctas--grid-container"><div class="ds-sticky-ctas--container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--sticky-ctas","attachmentId":104839598,"attachmentType":"pdf","workUrl":null}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--sticky-ctas","attachmentId":104839598,"attachmentType":"pdf","workUrl":null}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div><div class="ds-below-fold--grid-container"><div class="ds-work--container js-loswp-embedded-document"><div class="attachment_preview" data-attachment="Attachment_104839598" style="display: none"><div class="js-scribd-document-container"><div class="scribd--document-loading js-scribd-document-loader" style="display: block;"><img alt="Loading..." src="//a.academia-assets.com/images/loaders/paper-load.gif" /><p>Loading Preview</p></div></div><div style="text-align: center;"><div class="scribd--no-preview-alert js-preview-unavailable"><p>Sorry, preview is currently unavailable. You can download the paper by clicking the button above.</p></div></div></div></div><div class="ds-sidebar--container js-work-sidebar"><div class="ds-related-content--container"><h2 class="ds-related-content--heading">Related papers</h2><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="0" data-entity-id="10004309" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/10004309/Nonequilibrium_phase_transitions_and_finite_size_scaling_in_weighted_scale_free_networks">Nonequilibrium phase transitions and finite size scaling in weighted scale-free networks</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="24347886" href="https://independent.academia.edu/RobertJuhasz">Robert Juhasz</a></div><div class="ds-related-work--ctas"><button class="ds2-5-text-link 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Bhattacharjee</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physics Letters A, 2006</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Is small-world network disordered?","attachmentId":44719170,"attachmentType":"pdf","work_url":"https://www.academia.edu/13997424/Is_small_world_network_disordered","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/13997424/Is_small_world_network_disordered"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="4" data-entity-id="20480021" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/20480021/Discrete_surface_growth_process_as_a_synchronization_mechanism_for_scale_free_complex_networks">Discrete surface growth process as a synchronization mechanism for scale-free complex networks</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="20504163" href="https://independent.academia.edu/LidiaBraunstein">Lidia Braunstein</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical Review E, 2007</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Discrete surface growth process 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