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

Ken-Ichi Aoki·Keiichi Morikawa·Wataru Souma·Jun-ichi Sumi·Haruhiko Terao
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Abstract

The non-perturbative Wegner-Houghton renormalization group is analyzed by the local potential approximation in O(N) scalar theories in d-dimensions $(3\leq d\leq 4)$. 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 $O(ε)$ 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.

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Ken-Ichi Aoki, Keiichi Morikawa, Wataru Souma, Jun-ichi Sumi, Haruhiko Terao. 1996-12-24. The effectiveness of the local potential approximation in the Wegner-Houghton renormalization group. https://doi.org/10.1143/ptp.95.409

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