  We develop a semi-classical field method for the study of the weakly
interacting Bose gas at finite temperature, which, contrarily to the usual
classical 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 density
and the vortex pair distribution function. Insight in the physics of the system
is obtained by comparing the numerical results with the predictions of simple
analytical models. In particular, we calculate the activation energy required
to form a vortex pair at low temperature.
