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

The three-state majority-vote model with noise on Erdos-Renyi 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 q(c) is an increasing function of the mean connectivity z of the graph. The critical exponents beta/(v) over bar, gamma/(v) over bar and 1/(v) over bar are calculated for several values of the 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.