Discontinuous phase transition in an annealed multi-state majority-vote model

TL;DR

This paper investigates how increasing the number of states in a majority-vote model affects phase transition types, revealing that a three-state model exhibits a discontinuous transition with hysteresis, unlike the two-state model.

Contribution

The study extends the majority-vote model to multiple states and compares phase transition behaviors, highlighting the discontinuous transition and hysteresis in the three-state case.

Findings

Three-state model shows discontinuous phase transition.

Hysteresis behavior observed in the three-state model.

Two-state model exhibits continuous transition.

Abstract

In this paper, we generalize the original majority-vote (MV) model with noise from two states to arbitrary $q$ states, where $q$ is an integer no less than two. The main emphasis is paid to the comparison on the nature of phase transitions between the two-state MV (MV2) model and the three-state MV (MV3) model. By extensive Monte Carlo simulation and mean-field analysis, we find that the MV3 model undergoes a discontinuous order-disorder phase transition, in contrast to a continuous phase transition in the MV2 model. A central feature of such a discontinuous transition is a strong hysteresis behavior as noise intensity goes forward and backward. Within the hysteresis region, the disordered phase and ordered phase are coexisting.