Impact of site dilution and agent diffusion on the critical behavior of the majority-vote model.

In this work we study a modified version of the majority-vote model with noise. In particular, we consider a random diluted square lattice wherein a site is empty with a probability r. In order to analyze the critical behavior of the model, we perform Monte Carlo simulations on lattices with linear sizes up to L=140. By means of a finite-size scaling analysis we estimate the critical noises qc and the critical ratios β/ν, γ/ν, and 1/ν for some values of the probability r. Our results suggest that the critical exponents are different from those of the original model (r=0), but they are r independent (r>0). In addition, if we consider that agents can diffuse through the lattice, the exponents remain the same, suggesting a new universality class for the majority-vote model with noise. Based on the numerical data, we may conjecture that the values of the exponents in this universality class are β∼0.45, γ∼1.1, and ν∼1.0, which satisfy the scaling relation 2β+γ=dν=2.