  For a condensate in a one-dimensional ring geometry, we compare the
thermodynamic properties of three conceptually different classical field
techniques: stochastic dynamics, microcanonical molecular dynamics, and the
classical field method. Starting from non-equilibrium initial conditions, all
three methods approach steady states whose distribution and correlation
functions are in excellent agreement with an exact evaluation of the partition
function in the high-temperature limit. Our study helps to establish these
various classical field techniques as powerful non-perturbative tools for
systems at finite temperatures.
