Anisotropic scale invariance and the uniaxial Lifshitz point from the nonperturbative renormalization group

TL;DR

This paper uses the nonperturbative renormalization group with derivative expansion to analyze anisotropic scale invariance and Lifshitz points, providing estimates for critical exponents in three-dimensional uniaxial systems and comparing with existing methods.

Contribution

It demonstrates the existence of a Lifshitz fixed point with a non-classical anisotropy exponent and offers new estimates for critical exponents in 3D uniaxial Lifshitz points.

Findings

Existence of Lifshitz fixed point with $ heta<1/2$

Critical exponents estimated for (3,1) case

Comparison with perturbative and $1/N$ expansion results

Abstract

We employ the derivative expansion of the nonperturbative renormalization group to address the phenomenon of anisotropic scale invariance and the associated functional fixed points, also known as Lifshitz points, in systems characterized by a scalar order parameter. We demonstrate the existence of the Lifshitz fixed point featuring a non-classical value of the anisotropy exponent $\theta<1/2$ and provide estimates for values of a set of critical exponents in the physically most relevant case of the three-dimensional uniaxial Lifshitz point $(d,m)=(3,1)$, $m$ denoting the anisotropy index. We compare our predictions with existing estimates from perturbative expansions around dimensionality $d=4+\frac{1}{2}$ as well as those from the $1/N$ expansion.