Three-state majority-vote model on square lattice

Here, a non-equilibrium model with two states (-1, +1) and a noise q on simple square lattices proposed for M.J. Oliveira (1992) following the conjecture of up-down symmetry of Grinstein and colleagues (1985) is studied and generalized. This model is well-known, today, as the majority-vote model. They showed, through Monte Carlo simulations, that their obtained results fall into the universality class of the equilibrium Ising model on a square lattice. In this work, we generalize the majority-vote model for a version with three states, now including the zero state, (-1, 0, +1) in two dimensions. Using Monte Carlo simulations, we showed that our model falls into the universality class of the spin-1 (-1, 0, +1) and spin-1/2 Ising model and also agree with majority-vote model proposed for M.J. Oliveira (1992). The exponent ratio obtained for our model was gamma/nu = 1.77(3), beta/nu = 0.121(5), and 1/nu = 1.03(5). The critical noise obtained and the fourth-order cumulant were q(c) = 0.106(5) and U* = 0.62(3). (C) 2011 Elsevier B.V. All rights reserved.