Euclidean scalar field theory in the bi-local approximation

The blocking step of the renormalization group method is usually carried out by restricting it to fluctuations and to local blocked action. The tree-level, bilocal saddle point contribution to the blocking, defined by the infinitesimal decrease of the sharp cutoff in momentum space, is followed within the three dimensional Euclidean phi(6) model in this work. The phase structure is changed, new phases and relevant operators are found, and certain universality classes are restricted by the bilocal saddle point.