Interacting squares in arbitrary external field

Abstract

A model of a many-body system composed of squares with contact pair interactions in an arbitrary external field is presented. The formulation uses a mapping of the system onto polydisperse hard core mixtures. On the polydisperse level then, a simplified Hamiltonian function is specified. This assumption together with a further one about the global free energy functional for the pure hard core part of the idealized mixture make the model solvable. It is expected to hold for high temperatures, low densities, or low temperatures. The validity of the method of construction in the latter case is illustrated by a further application to a corresponding lattice system, for which exact results to compare with are readily available when the temperature is sufficiently low.