Existence of Pair Potential Corresponding to Specified Density and Pair Correlation
Existence of Pair Potential Corresponding to Specified Density and Pair Correlation
复制标题
指定密度对应的对势的存在性和对相关性
DOI：
10.1007/s11005-005-0343-9
复制
发表时间：
2005
影响因子：
1.2
通讯作者：
L. Koralov
中科院分区：
文献类型：
--
作者：
L. Koralov
给定一对相互作用势和一个活度值，我们可以考虑有限区域中的吉布斯分布
$$\Lambda \subset \mathbb{Z}^{d}$$。众所周知，对于较小的活度值，存在无限大的体积
$$（\Lambda \rightarrow \mathbb{Z}^{d}）$$极限吉布斯分布和无限体积相关函数。本文考虑了一个匡威问题，证明了给定ρ1和ρ2（x），其中ρ1是常数，ρ2（x）是上的函数
$$\mathbb{Z}^{d}$$，它们足够小，存在一个对势和一个活度值，其中ρ1是密度，ρ2（x）是对关联函数。
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.