Transição de fase no modelo do Votante Majoritário na presença de dois ruídos

  • Data: 30/11/15 às 11:00 h
  • Local: Sl A5-01
  • Apresentador: Allan Rodrigues Vieira - UFF

Resumo: Dinâmica de opiniões é um tópico interdisciplinar que tem atraído o interesse de físicos recentemente. Questões como a emergência de comportamentos coletivos e transições de fase em modelos de agentes têm sido amplamente investigadas. Neste seminário apresentaremos o modelo do votante majoritário, onde temos uma sociedade artificial em que cada indivíduo apresenta uma opinião (+1 ou -1) sobre um tópico - por exemplo uma pesquisa de voto entre dois candidatos, uma pesquisa entre dois produtos concorrentes, sim/não em um plebiscito, etc. Neste modelo um agente escolhido aleatoriamente interage com seus 4 primeiros vizinhos na rede quadrada (2D). Adicionaremos duas espécies de ruído: 1) o agente pode se opor à opinião majoritária dos vizinhos e adotar a opinião da minoria [1]; 2) o agente escolhe manter ou mudar de opinião independentemente de seus vizinhos [2]. Usando a taxa com a qual cada agente troca de opinião, fizemos uma aproximação de campo médio de forma que obtivemos analiticamente que a inclusão de cada um destes ruídos gera uma transição de fase com os mesmos expoentes do modelo de Ising em campo médio. Esses resultados foram obtidos de forma analítica e numérica. Por outro lado, obtivemos resultados numéricos para rede quadrada, e por meio da análise de tamanho finito estimamos os expoentes críticos, que novamente indicam o modelo está na mesma classe de universalidade do modelo de Ising.

[1] M. J. de Oliveira, J. Stat. Phys. 66, 273 (1992). [2] A. R. Vieira, N. Crokidakis, arxiv:1511.05111 (2015).

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