Rethinking Dimensional Regularization in Critical Phenomena

TL;DR

This paper introduces Functional Dimensional Regularization (FDR), a novel RG scheme that extends dimensional regularization beyond epsilon-expansion, enabling direct three-dimensional critical exponent calculations with improved convergence.

Contribution

The paper proposes FDR, a new functional RG method that combines DR's flexibility with functional RG's generality, applied to three-dimensional critical phenomena.

Findings

FDR allows direct computation of 3D critical exponents.

FDR shows faster convergence than existing functional RG methods.

FDR provides more accurate estimates of critical exponents.

Abstract

We show that it is possible to use dimensional regularization (DR) beyond the usual $\varepsilon$-expansion in the context of renormalization group (RG) calculations in Critical Phenomena. Based on this fact, we propose a new functional RG scheme - Functional Dimensional Regularization (FDR) - and apply it to a scalar theory in three dimensions. We compute the critical exponents of the Ising universality class directly in $d=3$ under various typical approximations. The method that emerges combines the agility typical of DR with the generality proper of functional RG. Moreover, at a given order of approximation, FDR seems to provide faster convergence and better estimates than other functional RGs.