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

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.

To be published in Condensed Matter Physics

References in corpus (3)

• Critical phenomena of the Majority voter model in a three dimensional cubic lattice
• Scaling at quantum phase transitions above the upper critical dimension
• Short-time Monte Carlo simulation of the majority-vote model on cubic lattices

Cited by in corpus (1)

• Stochastic thermodynamics of opinion dynamics