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 DP 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.

10 pages; based on invited talk at StatPhys 21

References in corpus (4)

• Critical behavior of a one-dimensional fixed-energy stochastic sandpile
• Anisotropic critical phenomena in parabolic geometries: the directed self-avoiding walk
• Continuously-variable survival exponent for random walks with movable partial reflectors
• Growth Exponent in the Domany-Kinzel Cellular Automaton

Cited by in corpus (11)

• Sandpiles with height restrictions
• The survival probability of a branching random walk in presence of an absorbing wall
• Activated Random Walkers: Facts, Conjectures and Challenges
• Absorbing-State Phase Transition for Driven-Dissipative Stochastic Dynamics on $Z$
• N-Site approximations and CAM analysis for a stochastic sandpile
• Self-organized Criticality and Absorbing States: Lessons from the Ising Model
• Path-integral representation for a stochastic sandpile
• Asymptotic behavior of the order parameter in a stochastic sandpile
• Critical behavior of an epidemic model of drug resistant diseases
• Uniform threshold for fixation of the stochastic sandpile model on the line
• Conserved sandpile with a variable height restriction