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Charge-unbinding transition in the two-dimensional classical Coulomb-plasma model by use of a variational Gaussian wave functional.

The charge-unbinding transitions in the two-dimensional classical Coulomb-plasma model are analyzed by use of the equivalence between the two-dimensional Coulomb plasma and (1+1)-dimensional quantum sine-Gordon models. The grand canonical potential and the screening length are obtained from the ground states of the (1+1)-dimensional quantum sine-Gordon model as derived by use of a variational Gaussian wave functional. We have shown that the charge-unbinding transition at small fugacity is a Kosterlitz-Thouless transition, while at large fugacity it is a first-order transition. The dependence of the potential on the mass is similar to that of the phenomenological Landau theory.