Voter model dynamics in complex networks: Role of dimensionality, disorder and degree distribution

TL;DR

This paper investigates how the voter model's ordering behavior in complex networks is influenced by network dimensionality, disorder, and degree distribution, revealing key factors affecting metastability and domain formation.

Contribution

It provides a comprehensive analysis of the voter model dynamics across various complex network structures, highlighting the impact of dimensionality, disorder, and hubs on ordering and metastability.

Findings

Ordering depends on the network's effective dimensionality.

Metastable state lifetime decreases with disorder and degree heterogeneity.

Hubs alter the scaling law of metastable state survival time.

Abstract

We analyze the ordering dynamics of the voter model in different classes of complex networks. We observe that whether the voter dynamics orders the system depends on the effective dimensionality of the interaction networks. We also find that when there is no ordering in the system, the average survival time of metastable states in finite networks decreases with network disorder and degree heterogeneity. The existence of hubs in the network modifies the linear system size scaling law of the survival time. The size of an ordered domain is sensitive to the network disorder and the average connectivity, decreasing with both; however it seems not to depend on network size and degree heterogeneity.