Majority-vote model on (3,4,6,4) and (3^4,6) Archimedean lattices

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 are q_c=0.091(2) and q_c=0.134(3) for (3,4,6,4) and (3^4,6) 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), 0.978(104) for (3^4,6) 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 dimensionality of the system [D_{eff}(3,4,6,4)=1.802(55) and D_{eff}(3^4,6)=1.860(34)] for these networks are reasonably close to the embedding dimension two.