Non-Hermitian Fermion Mapping for One-Component Plasma

The two-dimensional one-component logarithmic Coulomb gas is mapped onto a non-hermitian fermionic field theory. At $β=2$, the field theory is free. Correlation functions are calculated and a perturbation theory is discussed for extending to other $β$. A phase transition is found at the mean-field level at large $β$. Some results are extended to spaces of constant negative curvature.

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