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

Understand

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.