Existence of Pair Potential Corresponding to Specified Density and Pair Correlation

AbstractGiven a potential of pair interaction and a value of activity, one can consider the Gibbs distribution in a finite domain $$\Lambda \subset \mathbb{Z}^{d}$$ . It is well known that for small values of activity there exist the infinite volume $$(\Lambda \rightarrow \mathbb{Z}^{d})$$ limiting Gibbs distribution and the infinite volume correlation functions. In this paper we consider the converse problem – we show that given ρ1 and ρ2(x), where ρ1 is a constant and ρ2(x) is a function on $$\mathbb{Z}^{d}$$ , which are sufficiently small, there exist a pair potential and a value of activity, for which ρ1 is the density and ρ2(x) is the pair correlation function.

• Publication year

  2005

• Venue

  Letters in Mathematical Physics

• Publication date

  2005-02-01

• Fields of study

  Mathematics, Physics

• Identifiers
  DOI 10.1007/s11005-005-0343-9arXiv 0903.0432
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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