Three-state majority-vote model on square lattice

TL;DR

This study extends the Majority-Vote Model to include three states on a square lattice, demonstrating it belongs to the universality class of the spin-1 and spin-1/2 Ising models through Monte Carlo simulations.

Contribution

The paper introduces a three-state version of the Majority-Vote Model and confirms its universality class via Monte Carlo analysis, expanding understanding of non-equilibrium models.

Findings

Model falls into the universality class of spin-1 and spin-1/2 Ising models.

Critical noise level is approximately 0.106.

Critical exponents are estimated as γ/ν=1.77, β/ν=0.121, 1/ν=1.03.

Abstract

Here, the model of non-equilibrium model with two states ($-1,+1$) and a noise $q$ on simple square lattices proposed for M.J. Oliveira (1992) following the conjecture of up-down symmetry of Grinstein and colleagues (1985) is studied and generalized. This model is well-known, today, as Majority-Vote Model. They showed, through Monte Carlo simulations, that their obtained results fall into the universality class of the equilibrium Ising model on a square lattice. In this work, we generalize the Majority-Vote Model for a version with three states, now including the zero state, ($-1,0,+1$) in two dimensions. Using Monte Carlo simulations, we showed that our model falls into the universality class of the spin-1 ($-1,0,+1$) and spin-1/2 Ising model and also agree with Majority-Vote Model proposed for M.J. Oliveira (1992) . The exponents ratio obtained for our model was $\gamma/\nu =1.77(3)$, $\beta/\nu=0.121(5)$, and $1/\nu =1.03(5)$. The critical noise obtained and the fourth-order cumulant were $q_{c}=0.106(5)$ and $U^{*}=0.62(3)$.