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We develop a semi-classical field method for the study of the weaklyinteracting Bose gas at finite temperature, which, contrarily to the usualclassical field model, does not suffer from an ultraviolet cut-off dependence.We apply the method to the study of thermal vortices in spatially homogeneous,two-dimensional systems. We present numerical results for the vortex densityand the vortex pair distribution function. Insight in the physics of the systemis obtained by comparing the numerical results with the predictions of simpleanalytical models. In particular, we calculate the activation energy requiredto form a vortex pair at low temperature.

A semi-classical field method for the equilibrium Bose gas and application to thermal vortices in two dimensions