Majority-vote model on triangular, honeycomb and Kagomé lattices

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 q c = 0.089 ( 5 ) , q c = 0.078 ( 3 ) , and q c = 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 D eff = 1.96 ( 5 ) (honeycomb), D eff = 1.92 ( 4 ) (Kagomé), and D eff = 1.83 ( 5 ) (triangular) for these networks are just compatible to the embedding dimension two.