Modelo do votante majoritário de S estados com desordem controlada

Abstract

We investigate the nonequilibrium phase transition in the S-state majority-vote model for S =2,3,and 4. Each site, k, is characterized by a distinct noise threshold, q_k, which indicates its resistance to adopting the majority state of its N_v nearest neighbors. Precisely, this noise threshold is governed by a hyperbolic distribution, P(k) ∼ 1/k, bounded within the limits e^(-β) /2 < qk < 1/2. Here, the parameter β plays a pivotal role as it determines the extent of disorder in the system through the spread of the threshold distribution. Through Monte Carlo simulations and finite-size scaling analyses on regular square lattices, we deduced that the model undergoes a continuous order-disorder phase transition at a specific β=βc. Interestingly, the critical threshold exhibits a power-law decay, β_c∼N_v^(-δ) , as the number N_v of neighboring sites increases. From the leastsquares fits to the data sets results in δ=0.65±0.01 for S = 2,δ=0.93±0.01 for S=3,and δ=0.92±0.01 for S=4. Furthermore, the critical exponents β_e/ν_e and γ_e/ν_e are consistent with those found in the S-state Potts model.