On the equilibrium and time relaxation of a lattice gas in several boxes

Abstract

Lattice gases are investigated consisting of several boxes in which any particle interacts only with particles at its nearest neighbour sites within the same box, and particles can hop from one box to the other so that the total number is conserved. Two equal square lattices with attraction between particles in the same plane are simulated using the Monte Carlo method. While the equilibrium properties of this system are related simply to those for the plane, time relaxation differs. There are some interesting consequences, e.g., a consideration of two lattices may permit the more accurate determination of steady state properties in some cases, and novel phenomena may be exhibited. The nature of finite-size effects for low density is peculiar also. Further cases that exhibit interesting behaviour, even for one-dimensional boxes, are studied analytically by means of exact and mean-field solutions.