STUDY OF A LOCAL RG APPROXIMATION

A local approximation for the exact Wilson renormalization group (RG) equation is studied numerically and analytically. It is shown that at d = 3 it has a unique physical branch of the solution. The properties of this solutions and other physical solutions at 2 < d < 3 are discussed. The generation of nonlocalities is taken into account and it is shown that it leads to the existence of the usual second order phase transition in a 2D-system. The relation of this result to the Mermin-Wagner-Hohenberg theorem is discussed. The critical behaviour of an anisotropic system studied in local approximation and the possibility of fluctuation induced first order phase transitions are predicted in agreement with the epsilon-expansion result.