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 νare 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 $O(\epsilon )$ 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.

13 pages, latex, 6 figures

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