The two-dimensional Coulomb gas, vortex unbinding, and superfluid-superconducting films

Petter Minnhagen

doi:10.1103/RevModPhys.59.1001

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The two-dimensional Coulomb gas, vortex unbinding, and superfluid-superconducting films

Petter Minnhagen

DOI 10.1103/RevModPhys.59.1001 · Reviews of Modern Physics

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Abstract

The article reviews the two-dimensional Coulomb gas model and its connection to vortex fluctuations for a two-dimensional superfluid. The neutral and non-neutral versions of the Coulomb gas are discussed and the relation to an equivalent sine-Gordon field theory is given. The charge-unbinding picture is used to elucidate some essential properties of the Coulomb gas. Derivations of approximate renormalization equations are sketched and the phase transition for the neutral two-dimensional Coulomb gas is described. The Kosterlitz renormalization-group equations are reviewed in some detail. The vortex-Coulomb gas charge analogy is carefully explained. The connections between experiments for He4 films and superconducting films and the neutral and non-neutral versions of the Coulomb gas are outlined using concepts like the universal jump and the Coulomb gas scaling relations. The properties of a dynamical version of the Coulomb gas, corresponding to vortex dynamics, are discussed and related to experiments. An analogy with Maxwell's equations in two dimensions is also given.