Classical-field approximation for cold weakly interacting bosons without free parameters

The classical-field approximation to cold weakly interacting bosons allows for a unified treatment of condensed and uncondensed parts of the system. Until now, however, the quantitative predictions were limited by a dependence of the results on a grid chosen for numerical implementation of the method. In this paper, we propose replacing this unphysical ambiguity by an additional postulate: the temperature of the gas at thermal equilibrium should be the same as that of an ideal Bose gas with the same fraction of condensed atoms. As it turns out, with this additional assumption, nearly all atoms are within the classical fields, thus the method applies to the whole system.