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Majority-vote model on triangular, honeycomb and Kagomé lattices

Author

Listed:
  • Santos, J.C.
  • Lima, F.W.S.
  • Malarz, K.

Abstract

On Archimedean lattices, the Ising model exhibits spontaneous ordering. Three examples of these lattices of the majority-vote model with noise are considered and studied through extensive Monte Carlo simulations. The order/disorder phase transition is observed in this system. The calculated values of the critical noise parameter are qc=0.089(5), qc=0.078(3), and qc=0.114(2) for honeycomb, Kagomé and triangular lattices, respectively. The critical exponents β/ν, γ/ν and 1/ν for this model are 0.15(5), 1.64(5), and 0.87(5); 0.14(3), 1.64(3), and 0.86(6); 0.12(4), 1.59(5), and 1.08(6) for honeycomb, Kagomé and triangular lattices, respectively. These results differ from the usual Ising model results and the majority-vote model on so-far studied regular lattices or complex networks. The effective dimensionalities of the system Deff=1.96(5) (honeycomb), Deff=1.92(4) (Kagomé), and Deff=1.83(5) (triangular) for these networks are just compatible to the embedding dimension two.

Suggested Citation

  • Santos, J.C. & Lima, F.W.S. & Malarz, K., 2011. "Majority-vote model on triangular, honeycomb and Kagomé lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(2), pages 359-364.
    • Handle: RePEc:eee:phsmap:v:390:y:2011:i:2:p:359-364
    DOI: 10.1016/j.physa.2010.08.054
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