  We show how to achieve lattice-spacing independent results in numerical
simulations of finite-temperature stochastic scalar field theories. We
generalize the previous approach of hep-lat/9607026 by obtaining results which
are independent of the renormalization scale. As an application of our method,
we examine thermal phase mixing in the context of Ginzburg-Landau models with
short-range interactions. In particular, we obtain the lattice-spacing and
renormalization-scale independent critical value of the control parameter which
determines the free-energy barrier between the two low-temperature phases. We
also propose a simple procedure to extract the critical value of control
parameters for different choices of lattice spacing.
