The phase diagram and critical behavior of the three-state majority-vote model

The three-state majority-vote model with noise on Erdos-Renyi's random graphs has been studied. Using Monte Carlo simulations we obtain the phase diagram, along with the critical exponents. Exact results for limiting cases are presented, and shown to be in agreement with numerical values. We find that the critical noise qc is an increasing function of the mean connectivity z of the graph. The critical exponents beta/nu, gamma/nu and 1/nu are calculated for several values of connectivity. We also study the globally connected network, which corresponds to the mean-field limit z = N-1 -> infinity. Our numerical results indicate that the correlation length scales with the number of nodes in the graph, which is consistent with an effective dimensionality equal to unity.