Short-time Monte Carlo simulation of the majority-vote model on cubic lattices

TL;DR

This study uses short-time Monte Carlo simulations to precisely determine the critical point and exponents of the 3D majority-vote model, confirming its universality class matches that of the 3D Ising model.

Contribution

The paper introduces a new auxiliary function for critical point determination and provides accurate critical exponents for the 3D majority-vote model.

Findings

Critical point accurately located using the auxiliary function Ψ

Critical exponents calculated with finite-time scaling

Majority-vote model in 3D shares universality class with 3D Ising model

Abstract

We perform short-time Monte Carlo simulations to study the criticality of the isotropic two-state majority-vote model on cubic lattices of volume $N = L^3$, with $L$ up to $2048$. We obtain the precise location of the critical point by examining the scaling properties of a new auxiliary function $\Psi$. We perform finite-time scaling analysis to accurately calculate the whole set of critical exponents, including the dynamical critical exponent $z=2.027(9)$, and the initial slip exponent $\theta = 0.1081(1)$. Our results indicate that the majority-vote model in three dimensions belongs to the same universality class of the three-dimensional Ising model.