Scheme Independence and the Exact Renormalization Group

TL;DR

This paper investigates the computation of critical exponents in a three-dimensional scalar field theory using Wilson's exact renormalization group, highlighting scheme dependence issues at higher orders.

Contribution

It provides explicit calculations of critical exponents with derivative expansion and discusses scheme ambiguity at next-to-leading order.

Findings

Leading order results are cutoff independent.

Next-to-leading order results exhibit scheme dependence.

Confirmed a nontrivial relation between critical exponents.

Abstract

We compute critical exponents in a $Z_2$ symmetric scalar field theory in three dimensions, using Wilson's exact renormalization group equations expanded in powers of derivatives. A nontrivial relation between these exponents is confirmed explicitly at the first two orders in the derivative expansion. At leading order all our results are cutoff independent, while at next-to-leading order they are not, and the determination of critical exponents becomes ambiguous. We discuss the possible ways in which this scheme ambiguity might be resolved.