Universality class of nonequilibrium phase transitions with infinitely many-absorbing-states

TL;DR

This paper analyzes nonequilibrium phase transitions in systems with infinitely many absorbing states, identifying a critical dimension of 6 and providing critical exponents near the transition.

Contribution

It introduces a unified analysis of systems with many absorbing states and challenges the previous belief about the upper critical dimension being lower.

Findings

Critical dimension d_c=6 for anomalous scaling

Critical exponents derived in a 6-d expansion

Applicable to various models like contact process and sandpiles

Abstract

We consider systems whose steady-states exhibit a nonequilibrium phase transition from an active state to one -among an infinite number- absorbing state, as some control parameter is varied across a threshold value. The pair contact process, stochastic fixed-energy sandpiles, activated random walks and many other cellular automata or reaction-diffusion processes are covered by our analysis. We argue that the upper critical dimension below which anomalous fluctuation driven scaling appears is d_c=6, in contrast to a widespread belief (see Dickman cond-mat 0110043 for an overview). We provide the exponents governing the critical behavior close to or at the transition point to first order in a 6-d expansion.