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

TL;DR

This paper introduces a generalized Ising model with variable spin strength on scale-free networks, revealing new universality classes and exact solutions for thermodynamic behavior influenced by power-law distributions.

Contribution

It provides an exact solution for the model's partition function on complex networks with power-law distributions, highlighting the impact of variable node properties on phase transitions.

Findings

Thermodynamic functions are self-averaging in the annealed network approximation.

Derived critical behavior and logarithmic corrections at phase interfaces.

Identified new universality classes due to interplay of power-law distributions.

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 to 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.