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The Wilson-Polchinski exact renormalization group equation

C. Bervillier
(
- Saclay
)

May, 2004

7 pages

Published in:

Phys.Lett.A 332 (2004) 93-100

e-Print:

hep-th/0405025 [hep-th]

DOI:

10.1016/j.physleta.2004.09.037

Report number:

SACLAY-SPH-T04-058,
T04-058

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Abstract: (arXiv)

The critical exponent

\eta

is not well accounted for in the Polchinski exact formulation of the renormalization group (RG). With a particular emphasis laid on the introduction of the critical exponent

\eta

, I re-establish (after Golner, hep-th/9801124) the explicit relation between the early Wilson exact RG equation, constructed with the incomplete integration as cutoff procedure, and the formulation with an arbitrary cutoff function proposed later on by Polchinski. I (re)-do the analysis of the Wilson-Polchinski equation expanded up to the next to leading order of the derivative expansion. I finally specify a criterion for choosing the ``best'' value of

\eta

to this order. This paper will help in using more systematically the exact RG equation in various studies.

Note:

Some minor changes, a reference added, typos corrected

64.60.Ak
11.10.Gh
05.10.Cc
Exact renormalization group
Derivative expansion
Critical exponents
field theory: scalar
renormalization group: transformation
temperature: high
expansion: derivative

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