Revisiting the local potential approximation of the exact renormalization group equation

Abstract

The conventional absence of field renormalization in the local potential approximation (LPA) --implying a zero value of the critical exponent η-- is shown to be incompatible with the logic of the derivative expansion of the exact renormalization group (RG) equation. We present a LPA with η\neq 0 that strictly does not make reference to any momentum dependence. Emphasis is made on the perfect breaking of the reparametrization invariance in that pure LPA (absence of any vestige of invariance) which is compatible with the observation of a progressive smooth restoration of that invariance on implementing the two first orders of the derivative expansion whereas the conventional requirement (η=0 in the LPA) precluded that observation.

Final version, some misprints corrected

References in corpus (8)

• Fundamentals of the Exact Renormalization Group
• High-accuracy scaling exponents in the local potential approximation
• Analytic continuation of Taylor series and the two-point boundary value problems of some nonlinear ordinary differential equations
• Analytical approximation schemes for solving exact renormalization group equations. II Conformal mappings
• Analytical approximation schemes for solving exact renormalization group equations in the local potential approximation
• Remarks on Exact RG Equations
• Reparameterisation Invariance and RG equations: Extension of the Local Potential Approximation
• The Wilson exact renormalization group equation and the anomalous dimension parameter

Cited by in corpus (11)

• Tensor lattice field theory with applications to the renormalization group and quantum computing
• Background independent exact renormalization group for conformally reduced gravity
• Fixed point structure of the conformal factor field in quantum gravity
• Asymptotic safety of scalar field theories
• Scaling and superscaling solutions from the functional renormalization group
• The fate of non-polynomial interactions in scalar field theory
• The local potential approximation in the background field formalism
• Self-consistent renormalization group approach to continuous phase transitions in alloys. Application to ordering in $\beta$-brass
• Effective medium approach in the renormalization group theory of phase transitions
• Universal scaling dimensions for highly irrelevant operators in the Local Potential Approximation
• Exact renormalization group equation for lattice Ginzburg-Landau models adapted to the solution in the local potential approximation