Three-state majority-vote model on square lattice

Abstract

Here, the model of 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 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 exponents 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 $U^{\ast }=0.62(3)$.

13 pages, 6 figures

References in corpus (6)

• Sociophysics: A review of Galam models
• Majority-vote model on (3,4,6,4) and (3^4,6) Archimedean lattices
• The phase diagram and critical behavior of the three-state majority-vote model
• Majority-vote model on triangular, honeycomb and Kagome lattices
• Simulation of majority rule disturbed by power-law noise on directed and undirected Barabasi-Albert networks
• Persistence in the zero-temperature dynamics of the $Q$-states Potts model on undirected-directed Barabási-Albert networks and Erdös-Rényi random graphs

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• Three-state Majority-Vote Model on Barabási-Albert and Cubic Networks and the Unitary Relation for Critical Exponents