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Three-state majority-vote model on square lattice

Author

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  • Lima, F.W.S.

Abstract

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).

Suggested Citation

  • Lima, F.W.S., 2012. "Three-state majority-vote model on square lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1753-1758.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:4:p:1753-1758
    DOI: 10.1016/j.physa.2011.10.033
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    Cited by:

    1. Pickhardt, Michael & Seibold, Goetz, 2014. "Income tax evasion dynamics: Evidence from an agent-based econophysics model," Journal of Economic Psychology, Elsevier, vol. 40(C), pages 147-160.
    2. Takamitsu Watanabe, 2020. "A numerical study on efficient jury size," Palgrave Communications, Palgrave Macmillan, vol. 7(1), pages 1-7, December.

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