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 γ / ν = 1.77 ( 3 ) , β / ν = 0.121 ( 5 ) , and 1 / ν = 1.03 ( 5 ) . The critical noise obtained and the fourth-order cumulant were q c = 0.106 ( 5 ) and U ∗ = 0.62 ( 3 ) .