Majority-vote model on (3,12^2), (4,6,12) and (4,8^2) Archimedean lattices

TL;DR

This study investigates the critical properties of a modified majority-vote model on specific Archimedean lattices using Monte Carlo simulations, revealing distinct critical behavior from the Ising model and other networks.

Contribution

It introduces a variation of the majority-vote model with a different transition rate and analyzes its critical properties on Archimedean lattices, providing new insights into its phase transition behavior.

Findings

Critical temperatures determined for each lattice.

Critical exponents differ from Ising and other models.

Distinct phase transition behavior observed.

Abstract

On ($3,12^2$), ($4,6,12$) and ($4,8^2$) Archimedean lattices, the critical properties of majority-vote model are considered and studied using the Glauber transition rate proposed by Kwak {\it et all.} [Phys. Rev. E, {\bf 75}, 061110 (2007)] rather than the traditional majority-vote with noise [Jos\'e M\'ario de Oliveira, J. Stat. Phys. {\bf 66}, 273 (1992)]. The critical temperature and the critical exponents for this transition rate are obtained from extensive Monte Carlo simulations and with a finite size scaling analysis. The calculated values of the critical temperatures Binder cumulant are $T_c=0.363(2)$ and $U_4^*=0.577(4)$; $T_c=0.651(3)$ and $U_4^*=0.612(5)$; and $T_c=0.667(2)$ and $U_4^*=0.613(5)$ for ($3,12^2$), ($4,6,12$) and ($4,8^2$) lattices, respectively. The critical exponents $\beta/\nu$, $\gamma/\nu$ and $1/\nu$ for this model are $0.237(6)$, $0.73(10)$, and $ 0.83(5)$; $0.105(8)$, $1.28(11)$, and $1.16(5)$; $0.113(2)$, $1.60(4)$, and $0.84(6)$ for ($3,12^2$), ($4,6,12$) and ($4,8^2$) 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.