Modelo do voto da maioria com distribuição mista de ruído

• Ano de defesa: 2011
• Autor(a) principal: LIMA JÚNIOR, Aranildo Rodrigues de
• Orientador(a): FERREIRA, Tiago Alessandro Espínola
• Banca de defesa: SILVA, Luciano Rodrigues da, SOUZA, Adauto José Ferreira de, STOSIC, Borko
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal Rural de Pernambuco
• Programa de Pós-Graduação: Programa de Pós-Graduação em Biometria e Estatística Aplicada
• Departamento: Departamento de Estatística e Informática
• País: Brasil
• Palavras-chave em Português: Modelo do voto da maioria; Método de Monte Carlo; Grafo aleatório; Probabilidade mista
• Palavras-chave em Inglês: Majority-vote model; Monte Carlo method; Random graphs; Mixed probability distribution
• Área do conhecimento CNPq: CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA
• Link de acesso: http://www.tede2.ufrpe.br:8080/tede2/handle/tede2/4524

In the majority-vote model with noise, defined in a network, a given site (spin) assumes the posite state (sign) of the majority of its neighboring spins with probability q and it takes the same state with probability (1−q). The noise parameter q is homogeneous for all sites. In this work, we investigate a more general and realistic version of the majority-vote model, in which a given site i has its own noise parameter qi satisfying a mixed probability distribution. In this way, there is a heterogeneous distribution of noise among the sites in the network. We consider the case of a distribution defined by P(qi) = bd (qi)+(1−b)d (qi−q), where b is the fraction of sites without noise and q is taken from a Gaussian distribution. We perform Monte Carlo simulations on random graphs of different sizes and three average connectivity, for several values of the parameter b. We calculate the magnetization, the susceptibility and the Binder’s fourth-order cumulant as functions of q. We note that the system presents an order-disorder phase transition at a critical value of the parameter noise qc, which is an increasing function of the fraction of sites without noise. We use finite-size scaling theory to construct the phase diagram of the model and estimate the critical exponents b /n , g / nd 1/n . These exponents satisfy the hyperscaling relation with effective dimensionality equals to unity, for all values of average connectivity and b. Finally we conclude that, the majority-vote model with mixed distribution of noise on random graphs belongs to a different universality class from the model with homogeneous distribution of noise.