Logarithmic relaxations in a random-field lattice gas subject to gravity

A simple lattice-gas model with random fields and gravity is introduced to describe a system of grains moving in a disordered environment. Off-equilib rium relaxations of bulk density and its two time correlation functions are numerically found to show logarithmic time dependences and "aging" effects . Similarities with dry granular media are stressed. The connections with o ff-equilibrium dynamics in other kinds of "frustrated" lattice models in th e presence of a directional driving force (gravity) are discussed to single out the appearance of universal features in the relaxation process.