Generalized Ising model on a scale-free network: an interplay of power laws

Mariana Krasnytska; Bertrand Berche; Yurij Holovatch; Ralph Kenna

doi:10.3390/e23091175

Generalized Ising model on a scale-free network: an interplay of power laws

Mariana Krasnytska, Bertrand Berche, Yurij Holovatch, Ralph Kenna

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

51 Downloads (Pure)

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. We find the delicate interplay of the two power laws leads to new universality classes.

Original language	English
Article number	1175
Number of pages	18
Journal	Entropy
Volume	23
Issue number	9
DOIs	https://doi.org/10.3390/e23091175
Publication status	Published - 7 Sept 2021

Bibliographical note

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Funder

National Research Foundation of Ukraine, project 2020.01/0338 (M.K.) and by the National Academy of Sciences of Ukraine, project KP-KBK6541230 (Y.H)

Keywords

Ising model
scale-free network
self-averaging
steepest descent
Scale-free network
Self-averaging
Steepest descent

ASJC Scopus subject areas

Information Systems
Electrical and Electronic Engineering
Mathematical Physics
Physics and Astronomy (miscellaneous)

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10.3390/e23091175Licence: CC BY

PublishedFinal published version, 1.23 MBLicence: CC BY

Cite this

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title = "Generalized Ising model on a scale-free network: an interplay of power laws",

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 {\textquoteleft}+{\textquoteright} or {\textquoteleft}−{\textquoteright}, {\textquoteleft}up{\textquoteright} or {\textquoteleft}down{\textquoteright}, {\textquoteleft}yes{\textquoteright} or {\textquoteleft}no{\textquoteright}), 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.",

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author = "Mariana Krasnytska and Bertrand Berche and Yurij Holovatch and Ralph Kenna",

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AU - Berche, Bertrand

AU - Holovatch, Yurij

AU - Kenna, Ralph

N1 - This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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N2 - 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.

AB - 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.

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Generalized Ising model on a scale-free network: an interplay of power laws

Abstract

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Keywords

ASJC Scopus subject areas

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