Field theoretic approach to metastability in the contact process

Christophe Deroulers; Rémi Monasson

doi:10.1103/physreve.69.016126

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arXiv · cond-mat/0309637

Field theoretic approach to metastability in the contact process

Christophe Deroulers·Rémi Monasson

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Abstract

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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Christophe Deroulers, Rémi Monasson. 2005-08-10. Field theoretic approach to metastability in the contact process. https://doi.org/10.1103/physreve.69.016126

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