The Effectiveness of the Local Potential Approximation in the Wegner-Houghton Renormalization Group

Abstract

The non-perturbative Wegner-Roughton renormalization group is aiialyzed by the local potential approximation in O(N) scalar theories in d-dimensions (3sd:S4). The leading critical exponents 11 are calculated in order to investigate the effectiveness of the local potential approximation by comparing them with other non-perturbative methods. We show analytically that the local potential approximation gives the exact exponents 1,1p to O(E) in E-expansion and the leading in 1/N-expansion. We claim that this approximation offers fairly accurate results in the whole range of the parameter space of N and d. It is a great advantage of our method that no diverging expansions appear in the procedure.