Renormalized loop expansion to compute finite size effects of the constraint effective potential

In lattice φ4-theory close to the critical line, finite size effects can be computed by renormalized loop expansions. In order to do so, the constraint effective potential is computed to two loop order. Using this expression, we are able to extract results for renormalized masses and coupling constants from Multigrid Monte Carlo data of Mack and Meyer for the constraint effective potential close to the critical line, and compare them with the analytical results of Luescher and Weisz. Perfect agreement is found. (orig.)