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Article

Generalized Ising Model on a Scale-Free Network: An Interplay of Power Laws

1
Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, UA-79011 Lviv, Ukraine
2
\({{\mathbb L}^4}\) Collaboration & Doctoral College for the Statistical Physics of Complex Systems, Leipzig-Lorraine-Lviv-Coventry
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Laboratoire de Physique et Chimie Théoriques, Université de Lorraine, BP 70239, CEDEX, 54506 Vandœuvre-les-Nancy, France
4
Centre for Fluid and Complex Systems, Coventry University, Coventry CV1 5FB, UK
*
Author to whom correspondence should be addressed.
Academic Editor: Adam Lipowski
Entropy 2021, 23(9), 1175; https://doi.org/10.3390/e23091175
Received: 19 August 2021 / Revised: 1 September 2021 / Accepted: 3 September 2021 / Published: 7 September 2021
(This article belongs to the Special Issue Ising Model: Recent Developments and Exotic Applications)
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 universality classes. View Full-Text
Keywords: Ising model; scale-free network; self-averaging; steepest descent Ising model; scale-free network; self-averaging; steepest descent
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MDPI and ACS Style

Krasnytska, M.; Berche, B.; Holovatch, Y.; Kenna, R. Generalized Ising Model on a Scale-Free Network: An Interplay of Power Laws. Entropy 2021, 23, 1175. https://doi.org/10.3390/e23091175

AMA Style

Krasnytska M, Berche B, Holovatch Y, Kenna R. Generalized Ising Model on a Scale-Free Network: An Interplay of Power Laws. Entropy. 2021; 23(9):1175. https://doi.org/10.3390/e23091175

Chicago/Turabian Style

Krasnytska, Mariana, Bertrand Berche, Yurij Holovatch, and Ralph Kenna. 2021. "Generalized Ising Model on a Scale-Free Network: An Interplay of Power Laws" Entropy 23, no. 9: 1175. https://doi.org/10.3390/e23091175

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