Majority-vote model on a random lattice

Abstract

The stationary critical properties of the isotropic majority vote model on random lattices with quenched connectivity disorder are calculated by using Monte Carlo simulations and finite size analysis. The critical exponents γ and β are found to be different from those of the Ising and majority vote on the square lattice model and the critical noise parameter is found to be qc = 0.117 ± 0.005.

Majority-Vote on Directed Small-World Networks

“…J. M. Oliveira [13] showed that the majority-vote model defined on a regular lattice has critical exponents that fall into the same class of universality as the corresponding equilibrium Ising model. Campos et al [17] investigated the critical behavior of the majority-vote on small-world networks by rewiring the two-dimensional square lattice, Pereira et al [21] studied this model on Erdös-Rényi's random graphs, and Lima et al [18] also studied this model on Voronoy-Delaunay lattice and Lima on directed Barabási-Albert network [15]. The results obtained these authors show that the critical exponents of majority-vote model belong to different universality classes.…”

“…We consider the majority-vote model, on directed small-world networks, defined [13,20,18,21] by a set of "voters" or spins variables σ taking the values +1 or −1, situated on every site of an directed small-world networks with N = L × L sites, were L is the side of square lattice, and evolving in time by single spin-flip like dynamics with a probability w i given by…”

Controlling the Tax Evasion Dynamics via Majority-Vote Model on Various Topologies

“…The majority-vote model (MVM) is a nonequilibrium model proposed by M. J. Oliveira in 1992 [20] and defined by stochastic dynamics with local rules and with up-down symmetry on a regular lattice shows a second-order phase transition with critical exponents β, γ, and ν which characterize the system in the vicinity of the phase transition identical with those of the equilibrim Ising model [1] for regular lattices. Lima et al [23] studied MVM on VD random lattices with periodic boundary conditions. These lattices posses natural quenched disorder in their connections.…”

Majority-Vote on Directed Barabási–albert Networks

“…However, it was not evident that the exponent change was due to the disordered nature of the network or due to the presence of long-range interactions. Lima et al [6] studied the majority-vote model on Voronoi-Delaunay random lattices with periodic boundary conditions. These lattices posses natural quenched disorder in their conecctions.…”