Majority-vote model on (3,4,6,4) and (3(4),6) Archimedean lattices
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 are q(c) = 0.091(2) and q(c) = 0.134(3) for (3, 4, 6, 4) and (34, 6) Archimedean lattices, respectively. The critical exponents beta/nu, gamma/nu and 1/nu 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 [D-eff(314,614) = 1.802(55) and D-eff(3(4),6) = 1.860(34)] for these networks are reasonably close to the embedding dimension two.
monte carlo simulation phase transition critical exponents nonequilibrium