Elsevier

Physics Letters B

Volume 323, Issues 3–4, 17 March 1994, Pages 330-338
Physics Letters B

Gradient flows from an approximation to the exact renormalization group

https://doi.org/10.1016/0370-2693(94)91228-9Get rights and content

Abstract

Through appropriate projections of an exact renormalization group equation, we study fixed points, critical exponents and nontrivial renormalization group flows in scalar field theories in 2<d<4. The standard upper critical dimensions dk=2k(k−1), k=2,3,4, ...appear naturally encoded in our formalism, and for dimensions smaller but very close to dk our results match the ϵ-expansion. Within the coupling constant subspace of mass and quartic couplings and for any d, we find a gradient flow with two fixed points determined by a positive-definite metric and a c-function which is monotonically decreasing along the flow.

References (12)

  • K. Wilson et al.

    Phys. Rep.

    (1974)
    K. Wilson

    Rev. Mod. Phys.

    (1975)
  • N.F. Nicoll et al.

    Phys. Lett. A

    (1976)
  • A. Margaritis et al.

    Z. Phys. C

    (1988)
  • T. Morris, private...
  • C. Itzykson et al.
  • D.J. Wallace et al.

    Ann. Phys.

    (1975)
There are more references available in the full text version of this article.

Cited by (0)

This work is supported in part by funds provided by AEN 90-0033 Grant (Spain), and by M.E.C. (Spain).

1

On leave of absence from Nuclear Physics Institute, Moscow State University, 119899 Moscow, Russia.

View full text