Quantum Statistical Mechanics of Dissolving Vortices

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 $N^2$.

12 pages, 7 figures

References in corpus (4)

• On the L^2-metric of vortex moduli spaces
• Scattering theory and equation of state of a spherical two-dimensional Bose gas
• Quantum Statistical Mechanics of Vortices
• The geometry of the space of vortices on a two-sphere in the Bradlow limit