Optimal modularity for nucleation in network-organized Ising model

TL;DR

This paper investigates how the modular structure of coupled networks influences the nucleation process in the Ising model, revealing a transition in nucleation pathways and a nonmonotonic rate dependence on modularity.

Contribution

It introduces a novel method to study nucleation in modular networks and uncovers the optimal modularity for maximal nucleation rate.

Findings

Nucleation transitions from two-step to one-step with decreasing modularity.

Nucleation rate peaks at a moderate level of modularity.

Mean field analysis qualitatively supports simulation results.

Abstract

We study nucleation dynamics of Ising model in a topology that consists of two coupled random networks, thereby mimicking the modular structure observed in real-world networks. By introducing a variant of a recently developed forward flux sampling method, we efficiently calculate the rate and elucidate the pathway for nucleation process. It is found that as the network modularity becomes worse the nucleation undergoes a transition from two-step to one-step process. Interestingly, the nucleation rate shows a nonmonotonic dependency on the modularity, in which a maximal nucleation rate occurs at a moderate level of modularity. A simple mean field analysis is proposed to qualitatively illustrate the simulation results.