Sum rules for correlation functions of ionic mixtures in arbitrary dimension $d\geq 2$

TL;DR

This paper derives sum rules for correlation functions in multi-component ionic mixtures across arbitrary dimensions, revealing how these rules depend on the spatial dimension and connecting 2D cases to higher dimensions.

Contribution

It introduces a unified approach to derive sum rules for ionic mixtures in any dimension $d\,geq\,2$, linking 2D and higher-dimensional correlation properties.

Findings

Sum rules for moments of two-particle correlation functions are established.

Dependence of sum rules on spatial dimension $d$ is explicitly characterized.

Continuity near $d=2$ connects 2D correlation sum rules to higher dimensions.

Abstract

The correlations in classical multi-component ionic mixtures with spatial dimension $d\geq 2$ are studied by using a restricted grand-canonical ensemble and the associated hierarchy equations for the correlation functions. Sum rules for the first few moments of the two-particle correlation function are derived and their dependence on $d$ is established. By varying $d$ continuously near $d=2$ it is shown how the sum rules for the two-dimensional mixture are related to those for mixtures at higher $d$.