The effectiveness of the local potential approximation in the Wegner-Houghton renormalization group

Abstract

The non-perturbative Wegner-Houghton renormalization group is analyzed by the local potential approximation in O(N) scalar theories in d-dimensions (3≤d≤4). The leading critical exponents v 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 up to O(ε) in ε-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.