An Inverse Problem for Gibbs Fields with Hard Core Potential

Details An Inverse Problem for Gibbs Fields with Hard Core Potential An Inverse Problem for Gibbs Fields with Hard Core Potential

2009-03-03

arxiv.org/abs/0903.0433v1

Journal of Mathematical Physics, Vol 48, No 5 (2007)

Physics

Mathematical Physics

Scientific paper

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 $\mathbb{R}^d$). In this paper we consider a converse problem. Namely, we show that for a sufficiently small constant $\overline{\rho}_1$ and a sufficiently small function $\overline{\rho}_2(x)$, $x \in \mathbb{R}^d$, 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 $\overline{\rho}_1$ is the density and $\overline{\rho}_2$ is the pair correlation function of the corresponding Gibbs field.

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