{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,11]],"date-time":"2024-08-11T07:07:46Z","timestamp":1723360066193},"reference-count":66,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2021,9,7]],"date-time":"2021-09-07T00:00:00Z","timestamp":1630972800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"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 \u2018+\u2019 or \u2018\u2212\u2019, \u2018up\u2019 or \u2018down\u2019, \u2018yes\u2019 or \u2018no\u2019), 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 universality classes.<\/jats:p>","DOI":"10.3390\/e23091175","type":"journal-article","created":{"date-parts":[[2021,9,7]],"date-time":"2021-09-07T14:24:25Z","timestamp":1631024665000},"page":"1175","source":"Crossref","is-referenced-by-count":7,"title":["Generalized Ising Model on a Scale-Free Network: An Interplay of Power Laws"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"http:\/\/orcid.org\/0000-0002-0464-5741","authenticated-orcid":false,"given":"Mariana","family":"Krasnytska","sequence":"first","affiliation":[{"name":"Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, UA-79011 Lviv, Ukraine"},{"name":"\\({{\\mathbb L}^4}\\) Collaboration & Doctoral College for the Statistical Physics of Complex Systems, Leipzig-Lorraine-Lviv-Coventry"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-4254-807X","authenticated-orcid":false,"given":"Bertrand","family":"Berche","sequence":"additional","affiliation":[{"name":"\\({{\\mathbb L}^4}\\) Collaboration & Doctoral College for the Statistical Physics of Complex Systems, Leipzig-Lorraine-Lviv-Coventry"},{"name":"Laboratoire de Physique et Chimie Th\u00e9oriques, Universit\u00e9 de Lorraine, BP 70239, CEDEX, 54506 Vand\u0153uvre-les-Nancy, France"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-1125-2532","authenticated-orcid":false,"given":"Yurij","family":"Holovatch","sequence":"additional","affiliation":[{"name":"Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, UA-79011 Lviv, Ukraine"},{"name":"\\({{\\mathbb L}^4}\\) Collaboration & Doctoral College for the Statistical Physics of Complex Systems, Leipzig-Lorraine-Lviv-Coventry"},{"name":"Centre for Fluid and Complex Systems, Coventry University, Coventry CV1 5FB, UK"}]},{"ORCID":"http:\/\/orcid.org\/0000-0001-9990-4277","authenticated-orcid":false,"given":"Ralph","family":"Kenna","sequence":"additional","affiliation":[{"name":"\\({{\\mathbb L}^4}\\) Collaboration & Doctoral College for the Statistical Physics of Complex Systems, Leipzig-Lorraine-Lviv-Coventry"},{"name":"Centre for Fluid and Complex Systems, Coventry University, Coventry CV1 5FB, UK"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"883","DOI":"10.1103\/RevModPhys.39.883","article-title":"History of the Lenz-Ising Model","volume":"39","author":"Brush","year":"1967","journal-title":"Rev. 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