Finite Size Scaling and “perfect” actions: the three dimensional Ising model

Using Finite-Size Scaling techniques, we numerically show that the first irrelevant operator of the lattice λφ4 theory in three dimensions is (within errors) completely decoupled at λ=1.0. This interesting result also holds in the Thermodynamical Limit, where the renormalized coupling constant shows an extraordinary reduction of the scaling-corrections when compared with the Ising model. It is argued that Finite-Size Scaling analysis can be a competitive method for finding improved actions.