Tunable disorder on the <i>S</i>-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, qk, which indicates its resistance to adopting the majority state of its Nv nearest neighbors. Precisely, this noise threshold is governed by a hyperbolic distribution, P(k)∼1/k, bounded within the limits e-α/2<qk<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=αc. Interestingly, the critical threshold exhibits a power-law decay, αc∼Nv-δ, as the number Nv 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.