Tunable disorder on the S-state majority-voter model.

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 − α / 2 < q k < 1 / 2. Here, the parameter α 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 α = α c. Interestingly, the critical threshold exhibits a power-law decay, α c ∼ N v − δ , as the number N v of neighboring sites increases. From the least square fits to the data sets results in δ = 0.65 ± 0.01 for S = 2 , δ = 0.92 ± 0.01 for S = 3 , and δ = 0.93 ± 0.01 for S = 4. Furthermore, the critical exponents β / ν and γ / ν are consistent with those found in the S -state Potts model. [ABSTRACT FROM AUTHOR]