Majority-vote model on triangular, honeycomb and Kagome lattices

TL;DR

This study investigates the phase transition behavior of the majority-vote model with noise on three Archimedean lattices using Monte Carlo simulations, revealing unique critical parameters and exponents that differ from the Ising model.

Contribution

The paper provides the first detailed analysis of the majority-vote model with noise on honeycomb, Kagome, and triangular lattices, including critical noise values and exponents.

Findings

Identified critical noise parameters for each lattice.

Determined critical exponents that differ from the Ising model.

Estimated effective dimensionalities close to two.

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, Kagome and triangular lattices, respectively. The critical exponents beta/nu, gamma/nu and 1/nu 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, Kagome and triangular lattices, respectively. 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}= 1.96(5) (honeycomb), D_{eff} =1.92(4) (Kagome), and D_{eff}= 1.83(5) (triangular) for these networks are just compatible to the embedding dimension two.