Optimal modularity for nucleation in network-organized Ising model

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.