Majority-vote model on random graphs

Abstract

The majority-vote model with noise on Erdös-Rényi's random graphs has been studied. Monte Carlo simulations were performed to characterize the order-disorder phase transition appearing in the system. We found that the value of the critical noise parameter qc is an increasing function of the mean connectivity z of the random graph. The critical exponents beta/nu, gamma/nu, and 1/nu were calculated for several values of z, and our analysis yielded critical exponents satisfying the hyperscaling relation with effective dimensionality equal to unity.