Exact solution of the isotropic majority-vote model on complete graphs

TL;DR

This paper demonstrates that the isotropic majority-vote model on complete graphs satisfies detailed balance and provides an exact solution for its stationary distribution, challenging previous assumptions about its non-equilibrium nature.

Contribution

The authors derive the exact stationary distribution of the isotropic majority-vote model on complete graphs, showing it obeys detailed balance, unlike in other topologies.

Findings

Model satisfies detailed balance on complete graphs

Exact probability distribution depends only on magnetization

Numerical simulations confirm theoretical predictions

Abstract

The isotropic majority-vote (MV) model which, apart from the one-dimensional case, is thought to be non-equilibrium and violating the detailed balance condition. We show that this is not true, when the model is defined on a complete graph. In the stationary regime, the MV model on a fully connected graph fulfills the detailed balance. We derive the exact expression for the probability distribution of finding the system in a given spin configuration. We show that it only depends on the absolute value of magnetization. Our theoretical predictions are validated by numerical simulations.