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 $(3\le d\le 4)$. The leading critical exponents \nu are calculated in order to investigate the effectiveness of the local potential approximation by comparing them with the other non-perturbative methods. We show analytically that the local potential approximation gives the exact exponents up to $O(ϵ)$ in \epsilon-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.

Comments: 13 pages, latex, 6 figures