Nonequilibrium phase transitions in epidemics and sandpiles

Abstract

Nonequilibrium phase transitions between an active and an absorbing state are found in models of populations, epidemics, autocatalysis, and chemical reactions on a surface. While absorbing-state phase transitions fall generically in the directed-percolation universality class, this does not preclude other universality classes, associated with a symmetry or conservation law. An interesting issue concerns the dynamic critical behavior of models with an infinite number of absorbing configurations or a long memory. Sandpile models, the principal example of self-organized criticality (SOC), also exhibit absorbing-state phase transitions, with SOC corresponding to a particular mode of forcing the system toward its critical point.