Statistical mechanics of complex systems: rumor spreading in complex networks

Abstract

The interest among theoretical physicists in complex systems has grown in the last years. Among the problems that have called attention of physicists is the application of solid state, statistical mechanics and computational methods in the study of mechanisms governing opinion formation and propagation in a community. This study is justified by the observation that some scale properties of both proportional and majority elections seem universal, what suggests that some (few) interacting properties common to quite different communities are responsible for them. In this approach, individuals are compared to particles, and interact one with the other locally through a set of rules. One of those set of rules that has been employed with success in this context is the Sznajd model. This IC project intends to introduce the student Cesar Augustus Uliana Lima in this subject, as a motivation to the study of general concepts techniques of statistical mechanics, like phase transitions, dynamical systems, Monte Carlo simulations and complex networks. In order to achieve this goal, it includes an extensive study program, and the application of some of those techniques, mainly numerical, in a problem that has already been dealt with superficially by a master student under my supervision (Fabio Vannucchi), that is to perform a careful finite size scale analysis in some of their results. (AU)