Uma análise de escalonamento com o tamanho finito estendida aplicada ao modelo do voto da maioria

Abstract

The majority voter model has been simulated through the Monte Carlo method and a set of scaling functions has been determined, which are only expressed on terms of the scale variable x = ξL/L, where ξL is the correlation length of a size L finite system. The data for the obtained square networks in different noise values and several L sizes show an excellent collapse in every definition interval of the scale variable for both the correlation length and susceptibility. Knowing the scaling functions permits relating the value of a calculated parameter in a finite system for a given noise with the value of the same parameter in the thermodynamic limit (L → ∞) and the same noise. Therefore, it was capable to obtain the susceptibility values (χ) and the correlation length (ξ) from the majority voter model in the thermodynamic limit, in the critical region, which ξ ≫ 1. The critical parameters of the models were directly estimated from the χ ∼ t−γ and ξ ∼ t−ν, where t = 1 − qc/q is the distance from the critical point qc. It has been estimated qc = 0.076, ν = 1.22(1) and γ = 2.22(2), which shows that the values are compatible with the ones from the literature and that the system belongs to the same universality class of the 2D Ising model.