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 qc=0.106(5) and U∗=0.62(3).

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