The Partition Function of Multicomponent Log-Gases

TL;DR

This paper derives a new expression for the partition function of multicomponent one-dimensional log-gases with different charges at inverse temperature 1, extending classical identities to more complex ensembles.

Contribution

It introduces a Berezin integral representation for the partition function of multicomponent log-gases, generalizing de Bruijn identities to these ensembles.

Findings

Derived a Berezin integral formula for the partition function

Extended de Bruijn identities to multicomponent ensembles

Applicable to particles with different integer charges at inverse temperature 1

Abstract

We give an expression for the partition function of a one-dimensional log-gas comprised of particles of (possibly) different integer charge at inverse temperature {\beta} = 1 (restricted to the line in the presence of a neutralizing field) in terms of the Berezin integral of an associated non- homogeneous alternating tensor. This is the analog of the de Bruijn integral identities [3] (for {\beta} = 1 and {\beta} = 4) ensembles extended to multicomponent ensembles.