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The derivative expansion of the renormalization group

Abstract

By writing the flow equations for the continuum Legendre effective action (a.k.a. Helmholtz free energy) with respect to a particular form of smooth cutoff, and performing a derivative expansion up to some maximum order, a set of differential equations are obtained which at FPs (Fixed Points) reduce to non-linear eigenvalue equations for the anomalous scaling dimension {eta}. Illustrating this by expanding (single component) scalar field theory, in two, three and four dimensions, up to second order in derivatives, we show that the method is a powerful and robust means of discovering and quantifying non-perturbative continuum limits (continuous phase transitions). ((orig.)).
Authors:
Morris, T R [1] 
  1. Southampton Univ. (United Kingdom). Dept. of Physics
Publication Date:
Apr 01, 1995
Product Type:
Journal Article
Report Number:
CONF-9409269-
Reference Number:
SCA: 662110; PA: AIX-26:064351; EDB-95:132467; SN: 95001458366
Resource Relation:
Journal Name: Nuclear Physics B, Proceedings Supplements; Journal Volume: 42; Conference: Lattice `94, Bielefeld (Germany), 25 Sep - 1 Oct 1994; Other Information: PBD: Apr 1995
Subject:
66 PHYSICS; LATTICE FIELD THEORY; RENORMALIZATION; SERIES EXPANSION; ACTION INTEGRAL; ANOMALOUS DIMENSION; ASYMPTOTIC SOLUTIONS; DIFFERENTIAL CALCULUS; DIFFERENTIAL EQUATIONS; EIGENVALUES; FOUR-DIMENSIONAL CALCULATIONS; FREE ENERGY; NONLINEAR PROBLEMS; PARTITION FUNCTIONS; PHASE TRANSFORMATIONS; SCALAR FIELDS; THREE-DIMENSIONAL CALCULATIONS; TWO-DIMENSIONAL CALCULATIONS
OSTI ID:
101045
Country of Origin:
Netherlands
Language:
English
Other Identifying Numbers:
Journal ID: NPBSE7; ISSN 0920-5632; TRN: NL95FF391064351
Submitting Site:
NLN
Size:
pp. 811-814
Announcement Date:
Oct 05, 1995

Citation Formats

Morris, T R. The derivative expansion of the renormalization group. Netherlands: N. p., 1995. Web. doi:10.1016/0920-5632(95)00389-Q.
Morris, T R. The derivative expansion of the renormalization group. Netherlands. doi:10.1016/0920-5632(95)00389-Q.
Morris, T R. 1995. "The derivative expansion of the renormalization group." Netherlands. doi:10.1016/0920-5632(95)00389-Q. https://www.osti.gov/servlets/purl/10.1016/0920-5632(95)00389-Q.
@misc{etde_101045,
title = {The derivative expansion of the renormalization group}
author = {Morris, T R}
abstractNote = {By writing the flow equations for the continuum Legendre effective action (a.k.a. Helmholtz free energy) with respect to a particular form of smooth cutoff, and performing a derivative expansion up to some maximum order, a set of differential equations are obtained which at FPs (Fixed Points) reduce to non-linear eigenvalue equations for the anomalous scaling dimension {eta}. Illustrating this by expanding (single component) scalar field theory, in two, three and four dimensions, up to second order in derivatives, we show that the method is a powerful and robust means of discovering and quantifying non-perturbative continuum limits (continuous phase transitions). ((orig.)).}
doi = {10.1016/0920-5632(95)00389-Q}
journal = {Nuclear Physics B, Proceedings Supplements}
volume = {42}
journal type = {AC}
place = {Netherlands}
year = {1995}
month = {Apr}
}