Quenched mean-field theory for the majority-vote model on complex networks

TL;DR

This paper develops a quenched mean-field theory for the majority-vote model on complex networks, deriving critical noise analytically and validating the theory with simulations, showing improved accuracy over previous models especially for directed networks.

Contribution

It introduces a quenched mean-field approach for the MV model on networks, providing analytical critical noise calculations and demonstrating improved predictive performance.

Findings

Analytical critical noise derived from the largest eigenvalue of a modified adjacency matrix.

Quenched mean-field theory outperforms previous heterogeneous mean-field models.

Validated with extensive simulations on synthetic and real networks, especially for directed networks.

Abstract

The majority-vote (MV) model is one of the simplest nonequilibrium Ising-like model that exhibits a continuous order-disorder phase transition at a critical noise. In this paper, we present a quenched mean-field theory for the dynamics of the MV model on networks. We analytically derive the critical noise on arbitrary quenched unweighted networks, which is determined by the largest eigenvalue of a modified network adjacency matrix. By performing extensive Monte Carlo simulations on synthetic and real networks, we find that the performance of the quenched mean-field theory is superior to a heterogeneous mean-field theory proposed in a previous paper [Chen \emph{et al.}, Phys. Rev. E 91, 022816 (2015)], especially for directed networks.