Revisiting Groeneveld’s approach to the virial expansion

S. Jansen
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引用次数: 4

Abstract

A generalized version of Groeneveld's convergence criterion for the virial expansion and generating functionals for weighted $2$-connected graphs is proven. The criterion works for inhomogeneous systems and yields bounds for the density expansions of the correlation functions $\rho_s$ (a.k.a. distribution functions or factorial moment measures) of grand-canonical Gibbs measures with pairwise interactions. The proof is based on recurrence relations for graph weights related to the Kirkwood-Salsburg integral equation for correlation functions. The proof does not use an inversion of the density-activity expansion, however a Moebius inversion on the lattice of set partitions enters the derivation of the recurrence relations.
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再次回顾格林内菲尔德的病毒式扩张方法
证明了加权$2$连通图的虚展开和生成泛函的广义版Groeneveld收敛准则。该准则适用于非齐次系统,并给出具有成对相互作用的大正则吉布斯测度的相关函数$\rho_s$(又称分布函数或阶乘矩测度)的密度展开的界。该证明是基于与相关函数的Kirkwood-Salsburg积分方程相关的图权的递归关系。该证明没有使用密度-活度展开的反转,而是在集合分区的格上使用莫比乌斯反转来推导递推关系。
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