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arXiv · 0903.0432

The Existence of Pair Potential Corresponding to Specified Density and Pair Correlation

L. Koralov
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Abstract

Given a potential of pair interaction and a value of activity, one can consider the Gibbs distribution in a finite domain $Λ\subset \mathbb{Z}^d$. It is well known that for small values of activity there exist the infinite volume ($Λ\to \mathbb{Z}^d$) limiting Gibbs distribution and the infinite volume correlation functions. In this paper we consider the converse problem - we show that given $ρ_1$ and $ρ_2(x)$, where $ρ_1$ is a constant and $ρ_2(x)$ is a function on $\mathbb{Z}^d$, which are sufficiently small, there exist a pair potential and a value of activity, for which $ρ_1$ is the density and $ρ_2(x)$ is the pair correlation function.

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L. Koralov. 2009-03-03. The Existence of Pair Potential Corresponding to Specified Density and Pair Correlation. https://doi.org/10.1007/s11005-005-0343-9

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