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 journalArticlepeer-review

7 Citations (Scopus)
28 Downloads (Pure)


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 languageEnglish
Article number1175
Number of pages18
Issue number9
Publication statusPublished - 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.


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)


  • 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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