An Inverse Problem for Gibbs Fields with Hard Core Potential

It is well known that for a regular stable potential of pair interaction and a small value of activity one can define the corresponding Gibbs field (a measure on the space of configurations of points in R). In this paper we consider a converse problem. Namely, we show that for a sufficiently small constant ρ1 and a sufficiently small function ρ2(x), x ∈ R , that is equal to zero in a neighborhood of the origin, there exist a hard core pair potential, and a value of activity, such that ρ1 is the density and ρ2 is the pair correlation function of the corresponding Gibbs field.