The Partition Function of a Multi-Component Coulomb Gas on a Circle

Details The Partition Function of a Multi-Component Coulomb Gas on a Circle The Partition Function of a Multi-Component Coulomb Gas on a Circle

2007-12-28

arxiv.org/abs/0712.4371v2

J.Phys.A41:145003,2008

Physics

Condensed Matter

Statistical Mechanics

15 pages, 1 figure, v2: added discussion and references, version to appear in J. Phys. A

Scientific paper

10.1088/1751-8113/41/14/145003

We study a two-dimensional Coulomb gas consisting of a mixture of particles carrying various positive multiple integer charges, confined on a unit circle. We consider the system in the canonical and grand canonical ensembles, and attempt to calculate the partition functions analytically, using Toeplitz and confluent Vandermonde determinants. Just like in the simple one-component system (Dyson gas), the partition functions simplify at special temperature $\beta=2$, allowing us to find compact expressions for them.

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