Quantum Statistical Mechanics of Dissolving Vortices

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 ${\mathbb{C}\mathbb{P}}^N$ 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 $N^2$.