Modelo do voto da maioria com distribuição mista de ruído

Abstract

In the majority-vote model with noise, defined in a network, a given site (spin) assumes the posite state (sign) of the majority of its neighboring spins with probability q and it takes the same state with probability (1−q). The noise parameter q is homogeneous for all sites. In this work, we investigate a more general and realistic version of the majority-vote model, in which a given site i has its own noise parameter qi satisfying a mixed probability distribution. In this way, there is a heterogeneous distribution of noise among the sites in the network. We consider the case of a distribution defined by P(qi) = bd (qi)+(1−b)d (qi−q), where b is the fraction of sites without noise and q is taken from a Gaussian distribution. We perform Monte Carlo simulations on random graphs of different sizes and three average connectivity, for several values of the parameter b. We calculate the magnetization, the susceptibility and the Binder’s fourth-order cumulant as functions of q. We note that the system presents an order-disorder phase transition at a critical value of the parameter noise qc, which is an increasing function of the fraction of sites without noise. We use finite-size scaling theory to construct the phase diagram of the model and estimate the critical exponents b /n , g / nd 1/n . These exponents satisfy the hyperscaling relation with effective dimensionality equals to unity, for all values of average connectivity and b. Finally we conclude that, the majority-vote model with mixed distribution of noise on random graphs belongs to a different universality class from the model with homogeneous distribution of noise.