Quantum Statistical Mechanics of Dissolving Vortices

TL;DR

This paper calculates the quantum partition function for dissolving Abelian Higgs vortices on the moduli space, revealing different thermodynamic regimes and a non-extensive free energy at low temperatures.

Contribution

It provides an explicit spectral analysis of the quantum vortex partition function on the moduli space with new insights into thermodynamic behavior.

Findings

Derived the vortex gas pressure from the partition function.

Identified three temperature regimes with distinct behaviors.

Discovered non-extensive free energy proportional to N^2 at low temperatures.

Abstract

The quantum partition function for dissolving Abelian Higgs vortices is calculated explicitly, using spectral data for the Beltrami Laplacian on the $N$-vortex moduli space $\mathbb{CP}^N$ with a scaled Fubini--Study metric. From the partition function, the pressure of the vortex gas is derived. There are three asymptotic regimes -- High, Intermediate and Low Temperature. The phase crossover from Intermediate to Low Temperature is modelled by a Bessel function. In the Low Temperature regime the free energy is not extensive but is proportional to $N^2$.