Análise de fenômenos críticos no modelo Rock-Paper-Scissors

Abstract

This present work was developed with the purpose of analyzing critical phenomena in the Rock-Paper-Scissors model, consisting of three species and the empty site, initially distributed randomly in a square lattice, in which an active cell can interact with only one of its four neighbors (passive cells). The possible interactions are classified as motion (active and passive switch their positions), reproduction (active reproduces filling an empty site), or predation (active predates the passive generating an empty site). In summary, it is a cyclic interaction model with no privileged direction, however it shows signatures of a continuous phase transition from the diversity (symmetric phase) to uniformity (non symmetric phase). This way, we were motivated to study this type of system and analyze how the variation of one of its control parameters, the reproduction parameter µ, influences the system when µ → µc, where µc is the critical reproduction, and by performing numerical experiments identify to which universality class of the Rock-Paper-Scissors model with three species and the empty site belongs.