Nonequilibrium model on Archimedean lattices

Abstract

On (4, 6, 12) and (4, 82) Archimedean lattices, the critical properties of the majority-vote model are considered and studied using the Glauber transition rate proposed by Kwak et al. [Kwak et al., Phys. Rev. E, 75, 061110 (2007)] rather than the traditional majority-vote with noise [Oliveira, J. Stat. Phys. 66, 273 (1992)]. We obtain Tc and the critical exponents for this Glauber rate from extensive Monte Carlo studies and finite size scaling. The calculated values of the critical temperatures and Binder cumulant are Tc = 0.651(3) and U4* = 0.612(5), and Tc = 0.667(2) and U4* = 0.613(5), for (4, 6, 12) and (4, 82) lattices respectively, while the exponent (ratios) β/ν, γ/ν and 1/ν are respectively: 0.105(8), 1.48(11) and 1.16(5) for (4, 6, 12); and 0.113(2), 1.60(4) and 0.84(6) for (4, 82) lattices. The usual Ising model and the majority-vote model on previously studied regular lattices or complex networks differ from our new results.