Anomalous lifetime distributions and topological traps in ordering dynamics

TL;DR

This paper investigates how community structures in social interaction networks influence ordering dynamics and metastability, revealing anomalous lifetime distributions and topological traps that affect system behavior.

Contribution

It introduces analysis of metastability and lifetime distributions in voter and AB models on social networks, highlighting the impact of mesoscopic structures on dynamics.

Findings

Voter model exhibits metastable disordered states with characteristic lifetimes.

AB model shows power-law distribution of metastable state lifetimes.

Network mesoscopic structure causes topological traps affecting ordering.

Abstract

We address the role of community structure of an interaction network in ordering dynamics, as well as associated forms of metastability. We consider the voter and AB model dynamics in a network model which mimics social interactions. The AB model includes an intermediate state between the two excluding options of the voter model. For the voter model we find dynamical metastable disordered states with a characteristic mean lifetime. However, for the AB dynamics we find a power law distribution of the lifetime of metastable states, so that the mean lifetime is not representative of the dynamics. These trapped metastable states, which can order at all time scales, originate in the mesoscopic network structure.