The Wilson-Polchinski exact renormalization group equation

Abstract

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.

Some minor changes, a reference added, typos corrected

Cited by in corpus (18)

• Aspects of the Functional Renormalisation Group
• High-accuracy scaling exponents in the local potential approximation
• Universality and the Renormalisation Group
• Equivalence of Local Potential Approximations
• Analytical approximation schemes for solving exact renormalization group equations in the local potential approximation
• Optimization of field-dependent nonperturbative renormalization group flows
• Nonlinear Aspects of the Renormalization Group Flows of Dyson's Hierarchical Model
• Remarks on Exact RG Equations
• The fate of non-polynomial interactions in scalar field theory
• Revisiting the local potential approximation of the exact renormalization group equation
• Wilson-Polchinski exact renormalization group equation for O(N) systems: Leading and next-to-leading orders in the derivative expansion
• Reparameterisation Invariance and RG equations: Extension of the Local Potential Approximation
• Gradient flow exact renormalization group -- inclusion of fermion fields
• Renormalization Group Analysis of Turbulent Hydrodynamics
• Structure of Exact Renormalization Group Equations for field theory
• Exact Renormalization Group : A New Method for Blocking the Action
• Non-Perturbative Tachyon Potential from the Wilsonian Renormalization Group
• On the wave function renormalization for Wilson actions and their 1PI actions