Existence of an upper critical dimension in the majority voter model

Abstract

We study the critical properties of the majority voter model on d-dimensional hypercubic lattices. In two dimensions, the majority voter model belongs to the same universality class as that of the Ising model. However, the critical behaviors of the majority voter model on four dimensions do not exhibit mean-field behavior. Using the Monte Carlo simulation on d-dimensional hypercubic lattices, we obtain the critical exponents up to d=7, and find that the upper critical dimension is 6 for the majority voter model. We also confirm our results using mean-field calculation.