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 ≥ 5, the estimates of the exponents are close to the prediction d/2 when taking into account the dangerous irrelevant variable at the Gaussian 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.

Keywords

• critical phenomena
• equilibrium lattice models
• nonequilibrium lattice models
• finite-size scaling
• monte carlo methods