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).

Contribution to Lattice '94, 3 pages, uuencoded compressed postscript file

References in corpus (3)

• The Exact Renormalisation Group and Approximate Solutions
• Derivative Expansion of the Exact Renormalization Group
• On Truncations of the Exact Renormalization Group

Cited by in corpus (11)

• Optimization of the derivative expansion in the nonperturbative renormalization group
• On the Fixed-Point Structure of Scalar Fields
• A non perturbative approach of the principal chiral model between two and four dimensions
• Scaling solutions in the derivative expansion
• Universal behavior of coupled order parameters below three dimensions
• Revisiting the local potential approximation of the exact renormalization group equation
• Renormalization of composite operators
• Solutions of the Polchinski ERG equation in the O(N) scalar model
• Stability of fixed points and generalized critical behavior in multifield models
• Two Phases for Compact U(1) Pure Gauge Theory in Three Dimensions
• Gravitationally Induced UV Completion of an $O(N)$ Scalar Theory