2011/01/18 by Hanshuang Chen, Zhonghuai Hou
Mathematics · Physics and Astronomy · #Biology #Combinatorics #Complex Network Analysis Techniques #Complex network #Computer science #Ising model #Mathematics #Modular design #Modularity (biology) #Nucleation #Opinion Dynamics and Social Influence #Physics #Process (computing) #Statistical physics #Theoretical and Computational Physics #Thermodynamics #Topology (electrical circuits) #cond-mat.dis-nn #cond-mat.stat-mech #physics.soc-ph
paper · pdf · doi:10.1103/physreve.83.046124
6 pages, 5 figures
arxiv created 2011/01/18 · openalex publication_date 2011/04/26 · arxiv updated 2015/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the nucleation dynamics of the 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 the nucleation process. It is found that as the network modularity worsens the nucleation undergoes a transition from a two-step to one-step process. Interestingly, the nucleation rate shows a nonmonotonic dependence 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.