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 q(c) and the critical ratios beta/nu, gamma/nu, and 1/nu 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 beta similar to 0.45, gamma similar to 1.1, and nu similar to 1.0, which satisfy the scaling relation 2 beta + gamma = d nu = 2.