Lattice study of the Kink soliton and the zero-mode problem for phi4 in two dimensions

We study the $\lambda {\varphi }_{1+1}^4$ kink solion and the zero-mode contribution to the Kink soliton mass in regions beyond the semiclassical regime. The calculations are done in the non-trivial scaling region and where appropriate the results are compared with the continuum, semiclassical values. We show, as a function of parameter space, where the zero-mode contributions become significant.