The WilsonPolchinski exact renormalization group equation
Abstract
The critical exponent η 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 η, I reestablish (after Golner, hepth/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 WilsonPolchinski equation expanded up to the next to leading order of the derivative expansion. I finally specify a criterion for choosing the “best” value of η to this order. This Letter will help in using more systematically the exact RG equation in various studies.
 Publication:

Physics Letters A
 Pub Date:
 November 2004
 DOI:
 10.1016/j.physleta.2004.09.037
 arXiv:
 arXiv:hepth/0405025
 Bibcode:
 2004PhLA..332...93B
 Keywords:

 Exact renormalization group;
 Derivative expansion;
 Critical exponents;
 High Energy Physics  Theory;
 Condensed Matter  Other Condensed Matter
 EPrint:
 Some minor changes, a reference added, typos corrected