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Equivalence of local potential approximations

Equivalence of local potential approximations
Equivalence of local potential approximations
In recent papers it has been noted that the local potential approximation of the Legendre and Wilson-Polchinski flow equations give, within numerical error, identical results for a range of exponents and Wilson-Fisher fixed points in three dimensions, providing a certain "optimised" cutoff is used for the Legendre flow equation. Here we point out that this is a consequence of an exact map between the two equations, which is nothing other than the exact reduction of the functional map that exists between the two exact renormalization groups. We note also that the optimised cutoff does not allow a derivative expansion beyond second order.
field theories in lower dimensions, renormalization group
027-033
Morris, Tim R.
efe98b1a-0d67-42b9-8da9-7403e7a613f2
Morris, Tim R.
efe98b1a-0d67-42b9-8da9-7403e7a613f2

Morris, Tim R. (2005) Equivalence of local potential approximations. Journal of High Energy Physics, 7 (27), 027-033. (doi:10.1088/1126-6708/2005/07/027).

Record type: Article

Abstract

In recent papers it has been noted that the local potential approximation of the Legendre and Wilson-Polchinski flow equations give, within numerical error, identical results for a range of exponents and Wilson-Fisher fixed points in three dimensions, providing a certain "optimised" cutoff is used for the Legendre flow equation. Here we point out that this is a consequence of an exact map between the two equations, which is nothing other than the exact reduction of the functional map that exists between the two exact renormalization groups. We note also that the optimised cutoff does not allow a derivative expansion beyond second order.

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More information

Published date: 12 July 2005
Keywords: field theories in lower dimensions, renormalization group

Identifiers

Local EPrints ID: 57490
URI: http://eprints.soton.ac.uk/id/eprint/57490
PURE UUID: 6ae89287-27f1-4336-b3d3-b60468b2df05

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Date deposited: 14 Aug 2008
Last modified: 30 Jul 2019 17:43

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