Polchinski equation, reparameterization invariance and the derivative expansion

TL;DR

This paper investigates the invariance properties of fixed point actions in the exact renormalization group, applying the Polchinski equation at next-to-leading order to compute critical exponents for a scalar theory.

Contribution

It introduces a connection between anomalous dimensions and invariance properties, and applies the Polchinski equation at higher order to determine critical exponents.

Findings

Critical exponents: η=0.042, ν=0.622, ω=0.754

Demonstrates invariance properties in fixed point actions

Advances the use of the Polchinski equation in derivative expansions

Abstract

The connection between the anomalous dimension and some invariance properties of the fixed point actions within exact RG is explored. As an application, Polchinski equation at next-to-leading order in the derivative expansion is studied. For the Wilson fixed point of the one-component scalar theory in three dimensions we obtain the critical exponents \eta=0.042, \nu=0.622 and \omega=0.754.