Majority-vote model on triangular, honeycomb and Kagomé lattices

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=0.089(5), qc=0.078(3)qc=0.078(3), and qc=0.114(2)qc=0.114(2) for honeycomb, Kagomé and triangular lattices, respectively. The critical exponents β/νβ/ν, γ/νγ/ν and 1/ν1/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.