Time-dependent perturbation theory for nonequilibrium lattice models
Abstract
We develop a time-dependent perturbation theory for nonequilibrium interacting particle systems. We focus on models such as the contact process which evolve via destruction and autocatalytic creation of particles. At a critical value of the destruction rate there is a continuous phase transition between an active steady state and the vacuum state, which is absorbing. We present several methods for deriving series for the evolution starting from a single seed particle, including expansions for the ultimate survival probability in the super- and subcritical regions, expansions for the average number of particles in the subcritical region, and short-time expansions. Algorithms for computer generation of the various expansions are presented. Rather long series (24 terms or more) and precise estimates of critical parameters are presented.
- Publication:
-
Journal of Statistical Physics
- Pub Date:
- April 1993
- DOI:
- 10.1007/BF01048090
- Bibcode:
- 1993JSP....71...89J
- Keywords:
-
- Interacting particle systems;
- nonequilibrium critical points;
- series expansions;
- Padé
- analysis;
- Padé analysis