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

Kenichi Aoki | Zendy; K. Morikawa | Zendy; Wataru Souma | Zendy; J.-I. Sumi | Zendy; H. Terao | Zendy

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

Author(s) -

Kenichi Aoki,

K. Morikawa,

Wataru Souma,

J.-I. Sumi,

H. Terao

Publication year - 1996

Publication title -

progress of theoretical physics

Language(s) - English

Resource type - Journals

eISSN - 1347-4081

pISSN - 0033-068X

DOI - 10.1143/ptp.95.409

Subject(s) - physics , renormalization group , mathematical physics , renormalization , born–huang approximation , scalar (mathematics) , critical exponent , space (punctuation) , quantum electrodynamics , quantum mechanics , statistical physics , mathematical analysis , approximation error , mathematics , phase transition , geometry , linguistics , philosophy

The non-perturbative Wegner-Houghton renormalization group is analyzed by thelocal potential approximation in O(N) scalar theories in d-dimensions $(3\leqd\leq 4)$. The leading critical exponents \nu are calculated in order toinvestigate the effectiveness of the local potential approximation by comparingthem with the other non-perturbative methods. We show analytically that thelocal potential approximation gives the exact exponents up to $O(\epsilon )$ in\epsilon-expansion and the leading in 1/N-expansion. We claim that thisapproximation offers fairly accurate results in the whole range of theparameter space of N and d. It is a great advantage of our method that nodiverging expansions appear in the procedure.Comment: 13 pages, latex, 6 figure

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