How to Count Kinks: From the Continuum to the Lattice and Back

Abstract

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.

Comments: 7 pages, 5 PostScript figures, RevTeX. Revised version to appear in Physics Letters B. References and comparison with previous works added