  The study of nonlinear phenomena in systems with many degrees of freedom
often relies on complex numerical simulations. In trying to model realistic
situations, these systems may be coupled to an external environment which
drives their dynamics. For nonlinear field theories coupled to thermal (or
quantum) baths, discrete lattice formulations must be dealt with extreme care
if the results of the simulations are to be interpreted in the continuum limit.
Using techniques from renormalization theory, a self-consistent method is
presented to match lattice results to continuum models. As an application,
symmetry restoration in $\phi^4$ models is investigated.
