Field-theoretic approach to metastability in the contact process

The out-of-equilibrium distribution of densities of particles in the contact process on large regular lattices with degree z using a quantum field-theoretic formulation for the evolution operator was calculated. The calculation was based on a perturbative calculation of the effective potential for the density and an instantonic field. In powers of 1/z, corrections to the mean-field distribution of densities of particles in the out-of-equilibrium stationary state were derived. It was shown that the results for typical and rare fluctuation properties are in good agreement with numerical simulations carried out on D-dimensional hypercubic and Cayley lattices.