Field theoretic approach to metastability in the contact process

Details Field theoretic approach to metastability in the contact process Field theoretic approach to metastability in the contact process

2003-09-27

arxiv.org/abs/cond-mat/0309637v2

Physical Review E 69 (2004) 016126

Physics

Condensed Matter

Statistical Mechanics

Final published version; 20 pages, 5 figures

Scientific paper

10.1103/PhysRevE.69.016126

A quantum field theoretic formulation of the dynamics of the Contact Process on a regular graph of degree z is introduced. A perturbative calculation in powers of 1/z of the effective potential for the density of particles phi(t) and an instantonic field psi(t) emerging from the quantum formalism is performed. Corrections to the mean-field distribution of densities of particles in the out-of-equilibrium stationary state are derived in powers of 1/z. Results for typical (e.g. average density) and rare fluctuation (e.g. lifetime of the metastable state) properties are in very good agreement with numerical simulations carried out on D-dimensional hypercubic (z=2D) and Cayley lattices.

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