  We investigate the matching between (1+1)-dimensional nonlinear field
theories coupled to an external stochastic environment and their lattice
simulations. In particular, we focus on how to obtain numerical results which
are lattice-spacing independent, and on how to extract the correct effective
potential which emerges from the simulations. As an application, we study the
thermal production of kink-antikink pairs, obtaining a number density of pairs
which is lattice-spacing independent and the effective barrier for pair
production, i.e., the effective kink mass.
