How does degree heterogeneity affect nucleation of Ising model on complex networks?

TL;DR

This paper explores how the heterogeneity in node connectivity within complex networks influences the rate of phase transition nucleation in the Ising model, revealing nontrivial effects dependent on external field strength.

Contribution

It introduces a heterogeneous mean-field theory to evaluate nucleation barriers and demonstrates the nonmonotonic impact of degree heterogeneity on nucleation rates.

Findings

Nucleation rate decreases with increasing heterogeneity under weak external fields.

Nucleation rate shows a maximum at intermediate heterogeneity levels under strong external fields.

Theoretical estimates align qualitatively with simulation results.

Abstract

We investigate the nucleation of Ising model on complex networks and focus on the role played by the heterogeneity of degree distribution on nucleation rate. Using Monte Carlo simulation combined with forward flux sampling, we find that for a weak external field the nucleation rate decreases monotonically as degree heterogeneity increases. Interestingly, for a relatively strong external field the nucleation rate exhibits a nonmonotonic dependence on degree heterogeneity, in which there exists a maximal nucleation rate at an intermediate level of degree heterogeneity. Furthermore, we develop a heterogeneous mean-field theory for evaluating the free-energy barrier of nucleation. The theoretical estimations are qualitatively consistent with the simulation results. Our study suggests that degree heterogeneity plays a nontrivial role in the dynamics of phase transition in networked Ising systems.