Finite-Size Scaling of the majority-voter model above the upper critical dimension

TL;DR

This study uses Monte Carlo simulations to analyze the finite-size scaling behavior of the majority-voter model across dimensions 2 to 7, revealing that its upper critical dimension is 4, similar to the Ising model, contrary to previous claims.

Contribution

The paper demonstrates that the upper critical dimension of the majority-voter model is 4, not 6, by analyzing critical exponents and universal quantities across multiple dimensions.

Findings

Critical exponents align with the Ising model.

Logarithmic corrections at dimension 4.

Upper critical dimension is 4, not 6.

Abstract

The majority-voter model is studied by Monte Carlo simulations on hypercubic lattices of dimension $d=2$ to 7 with periodic boundary conditions. The critical exponents associated to the Finite-Size Scaling of the magnetic susceptibility are shown to be compatible with those of the Ising model. At dimension $d=4$, the numerical data are compatible with the presence of multiplicative logarithmic corrections. For $d\ge 5$,the estimates of the exponents are close to the prediction $d/2$ when taking into account the dangerous irrelevant variable at theGaussian fixed point. Moreover, the universal values of the Binder cumulant are also compatible with those of the Ising model. This indicates that the upper critical dimension of the majority-voter model is not $d_c=6$ as claimed in the literature, but $d_c=4$ like the equilibrium Ising model.