Noise induced phase transition in the $S$-state block voter model

TL;DR

This study investigates the phase transition behavior of the $S$-state block voter model on square lattices, revealing a change from continuous to discontinuous transitions at a critical number of states and establishing universality class correspondence.

Contribution

It introduces a detailed analysis of the phase transition types and critical behavior of the $S$-state block voter model, including universality class identification and long-range exponent estimation.

Findings

Continuous transition for S ≤ 4, discontinuous for S ≥ 5.

Model belongs to the same universality class as the 2D S-state Potts model.

Estimated long-range exponents for magnetization and susceptibility.

Abstract

We use Monte Carlo simulations and finite-size scaling theory to investigate the phase transition and critical behavior of the $S$-state block voter model on square lattices. It is shown that the system exhibits an order-disorder phase transition at a given value of the noise parameter, which changes from a continuous transition for $S\le4$ to a discontinuous transition for $S\ge5$. Moreover, for the cases of continuous transition, the calculated critical exponents indicate that the present studied nonequilibrium model system is in the same universality class of its counterpart equilibrium two-dimensional S-state Potts model. We also provide a first estimation of the long-range exponents governing the dependence on the range of interaction of the magnetization, the susceptibility, and the derivative of Binder's cumulant.