Quantum statistical mechanics of dissolving Abelian Higgs vortices

The quantum partition function for Abelian Higgs vortices at high density—the regime of dissolving vortices—is calculated explicitly, using spectral data for the Beltrami Laplacian on the N-vortex moduli space CPN 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.

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