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Prog. Theor. Phys. Vol. 95 No. 2 (1996) pp. 409-420

[ Full Text PDF : FREE ACCESS (557K) ]

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

Ken-Ichi Aoki, Keiichi Morikawa, Wataru Souma, Jun-Ichi Sumi and Haruhiko Terao

Department of Physics, Kanazawa University, Kanazawa 920-11

(Received November 6, 1995)

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 ν 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.


URL : http://ptp.ipap.jp/link?PTP/95/409/
DOI : 10.1143/PTP.95.409

[ Full Text PDF : FREE ACCESS (557K) ] Citation:

References:

  1. K. G. Wilson and J. B. Kogut, Phys. Rep. 12 (1974), 75[CrossRef].
  2. F. J. Wegner and A. Houghton, Phys. Rev. A8 (1973), 401[APS].
  3. J. Polchinski, Nucl. Phys. B231 (1984), 269.
  4. C. Wetterich, Phys. Lett. B301 (1993), 90.
  5. M. Alford, Phys. Lett. B336 (1994), 237.
    N. Tetradis and C. Wetterich, Nucl. Phys. B422 (1994), 541.
  6. A. Hasenfratz and P. Hasenfratz, Nucl. Phys. B270[FS16] (1986), 687.
  7. T. R. Morris, Phys. Lett. B334 (1994), 355.
  8. K.-I. Aoki, K. Morikawa, W. Souma, J.-I. Sumi and H. Terao, in preparation.
  9. K. G. Wilson and M. E. Fisher, Phys. Rev. Lett. 28 (1972), 240[APS].
  10. A. A. Vladimirov, D. I. Kazakov and O. V. Tarasov, Sov. Phys. JETP 50 (1979), 521.
  11. H. Kleinert, J. Neu, V. Schulte-Frohlinde, K. G. Chetyrkin and S. A. Larin, hep-th/9503230[e-print arXiv].
  12. L. N. Lipatov, Sov. Phys. JETP 45 (1977), 216.
    E. Brezin, J. C. Le Guillou and J. Zinn-Justin, Phys. Rev. D15 (1977), 1544[APS].
  13. J. C. Le Guillou and J. Zinn-Justin, Phys. Rev. B21 (1980), 3976[APS].
    J. Zinn-Justin, Quantum Field Theory and Critical Phenomena (Oxford University Press, 1989).
  14. R. Reuter, N. Tetradis and C. Wetterich, Nucl. Phys. B401 (1993), 567.
  15. R. Fukuda and E. Kyriakopoulos, Nucl. Phys. B85 (1975), 354.
    R. Fukuda, Prog. Theor. Phys. 56 (1976), 258[PTP].
    L. O'raifertaigh, A. Wipf and H. Yoneyama, Nucl. Phys. B271 (1986), 653.
  16. H. E. Stanlay, Phys. Rev. 176 (1968), 718[APS].
  17. R. Abe, Prog. Theor. Phys. 49 (1973), 1877[PTP].
    Y. Okabe and M. Oku, Prog. Theor. Phys. 60 (1978), 1277, [PTP]1287.
    A. N. Vasilev, Y. M. Pismak and Y. R. Khonkonen, Theor. Math. Phys. 46 (1981), 104; 47 (1981), 465.
  18. P. Butera and M. Comi, hep-lat/9505027 (IFUM-TH-498)[e-print arXiv].
  19. T. R. Morris, Phys. Lett. B329 (1994), 241.
  20. T. R. Morris, Int. J. Mod. Phys. A9 (1994), 2411.
    T. R. Morris, hep-th/9508017 (SHEP 95-21)[e-print arXiv].
  21. P. Hasenfratz and J. Nager, Z. Phys. C37 (1988), 477.
    T. E. Clark, B. Haeri and S. T. Love, Nucl. Phys. B402 (1993), 628.
    T. E. Clark, B. Haeri, S. T. Love, M. A. Walker and W. T. A. ter Veldhuis, Phys. Rev. D50 (1994), 606[APS].
  22. K.-I. Aoki, K. Shimizu, W. Souma, H. Terao and M. Tomoyose, in preparation.

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