MAJORITY-VOTE MODEL ON (3, 4, 6, 4) AND (34, 6) ARCHIMEDEAN LATTICES

F. W. S. Lima () and K. Malarz ()
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F. W. S. Lima: Departamento de Física, Universidade Federal do Piauí, 57072-970 Teresina, Piauí, Brazil
K. Malarz: Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, PL-30059 Kraków, Poland

International Journal of Modern Physics C (IJMPC), 2006, vol. 17, issue 09, 1273-1283

Abstract: On Archimedean lattices, the Ising model exhibits spontaneous ordering. Two 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 areqc= 0.091(2)andqc= 0.134(3)for (3, 4, 6, 4) and (34, 6) Archimedean lattices, respectively. The critical exponents β/ν, γ/ν and 1/ν for this model are 0.103 (6), 1.596 (54), 0.872 (85) for (3, 4, 6, 4) and 0.114 (3), 1.632 (35), 0.98 (10) for (34, 6) Archimedean lattices. These results differs 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(3, 4, 6, 4) = 1.802(55)andDeff(34, 6) = 1.860(34)] for these networks are reasonably close to the embedding dimension two.

Keywords: Monte Carlo simulation; critical exponents; phase transition; non-equilibrium; 05.10.Ln; 05.70.Fh; 64.60.Fr (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (1)

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DOI: 10.1142/S0129183106009849

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