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

TL;DR

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

Contribution

It provides the first detailed analysis of the majority-vote model on (3,4,6,4) and (3^4,6) Archimedean lattices, highlighting differences from the Ising model and other networks.

Findings

Critical noise parameters q_c=0.091(2) and 0.134(3) for the two lattices.

Distinct critical exponents from the Ising model.

Effective dimensionality close to two.

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.