Modelo do votante majoritário de S estados com desordem controlada

• Ano de defesa: 2025
• Autor(a) principal: Nascimento, Francisco Israel Alves do
• Orientador(a): Andrade Júnior, José Soares de
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Link de acesso: http://repositorio.ufc.br/handle/riufc/81347
• topic: Transição de fase de não equilíbrio; Modelo do votante majoritário; Redes regulares; Simulações de Monte Carlo; Expoentes críticos; Decaimento em lei de potência; Nonequilibrium phase transition; Majority-vote model; Monte Carlo simulations; Critical exponents; Power-law decay

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.