Abstract
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 Rd). In this paper we consider a converse problem. Namely, we show that for a sufficiently small constant ρ¯1 and a sufficiently small function ρ¯2(x), x∈Rd, 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 ρ¯1 is the density and ρ¯2 is the pair correlation function of the corresponding Gibbs field.
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