Field theoretic approach to metastability in the contact process

Christophe Deroulers (1) , Rémi Monasson (1, 2)

1 LPTENS - Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure]
2 LPTH - Laboratoire de Physique Théorique

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.

Mots clés: metastability; contact process; large deviation function

Domaines: Mécanique statistique [cond-mat.stat-mech]

Christophe Deroulers, Rémi Monasson. Field theoretic approach to metastability in the contact process. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2004, 69, pp.016126. ⟨10.1103/PhysRevE.69.016126⟩. ⟨hal-00000638v2⟩