A systematical improvement of the migdal recursion formula

We construct a new perturbative expansion whose zeroth-order approximation gives the Migdal-Kadanoff recursion equations. By this expansion it is therefore possible to improve systematically the Migdal-Kadanoff results. The first-order corrections are computed for the Ising and bond percolation models. The second-order corrections are computed only for the two-dimensional Ising model. Our method can be easily extended to other systems like the non-linear σ model or gauge theories.