Nucleation pathways on complex networks

TL;DR

This paper investigates how the structure of complex networks influences the pathways of nucleation in the Ising model, revealing distinct mechanisms in homogeneous versus heterogeneous networks using advanced sampling methods.

Contribution

It introduces a detailed analysis of nucleation pathways on different network topologies, highlighting the impact of network heterogeneity on nucleation mechanisms.

Findings

Homogeneous networks have a dominant nucleating cluster forming gradually.

Heterogeneous networks exhibit many small clusters merging suddenly.

Network heterogeneity determines the nucleation pathway.

Abstract

Identifying nucleation pathway is important for understanding the kinetics of first-order phase transitions in natural systems. In the present work, we study nucleation pathway of the Ising model in homogeneous and heterogeneous networks using the forward flux sampling method, and find that the nucleation processes represent distinct features along pathways for different network topologies. For homogeneous networks, there always exists a dominant nucleating cluster to which relatively small clusters are attached gradually to form the critical nucleus. For heterogeneous ones, many small isolated nucleating clusters emerge at the early stage of the nucleation process, until suddenly they form the critical nucleus through a sharp merging process. By analyzing the properties of the nucleating clusters along the pathway, we show that the main reason behind the different routes is the heterogeneous character of the underlying networks.