DOI
Documento
Autor
Nome completo
Elias José Portes Biral
E-mail
Área do Conhecimento
Data de Defesa
Imprenta
São Carlos, 2016
Fontanari, Jose Fernando (Presidente)
Campo Júnior, Vivaldo Leiria
Ferreira, Cláudia Pio
Título em português
O limite termodinâmico do modelo de Axelrod unidimensional de duas características e dois estados
Palavras-chave em português
Dinâmica cultural
Mecânica estatística
Modelo de Axelrod
Simulações de Monte Carlo
Resumo em português
Título em inglês
The thermodynamic limit of the one-dimensional Axelrod model with two features and two states
Palavras-chave em inglês
Axelrod model
Culture dynamics
Monte Carlo simulations
Statistical mechanics
Resumo em inglês
In the mid 1990s, the political scientist Robert Axelrod proposed an agent based-model of cultural dissemination, in which agents interact locally according to the principles of homophily and social influence, aiming at answering the question: "If people interact with each other and, through the interaction, become more similar, why are there cultural differences in our society?". Each agent is considered as an element of an array (a site in a lattice) and is modeled by a list of F cultural features, each of which assuming q possible states. This list is the cultural identity of the agent. The initial cultural identities of each agent are set randomly with equal probability for the qF different identities. At each time we pick an agent at random (the target agent) as well as one of its neighbors. These two agents interact with probability equal to their cultural similarity, defined as the fraction of identical features in their cultural lists. The more similar they are, the greater the likelihood of their interaction - this is the homophily principle. An interaction consists of selecting at random one of the distinct features, and making the state of the selected feature of the target agent equal to the corresponding state of its neighbor - this is the social influence principle. This procedure is repeated until the system is frozen into an absorbing configuration. We observe monocultural absorbing configurations, in which all agents have the same cultural identity, and multicultural configurations, in which there are different cultural domains in the lattice. In the one-dimensional model with F = q = 2, however, Monte Carlo simulations show convergence to the monocultural configurations in about 30% of the choices of the initial conditions, while the exact analytical results indicate that the monocultural convergence should always happen. In this thesis, we study the one-dimensional Axelrod model for F = q = 2 using Monte Carlo simulations. We show that the discrepancy between the simulations and the exact results is due to the non-commutation of the thermodynamic limit, in which the chain size goes to infinity, and the time-asymptotic limit, in which the simulation time goes to infinity. Our results offer a better understanding of the one-dimensional Axelrod model and promote the importance of the agreement between theory and simulations in science.

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Data de Publicação
2016-04-29

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