New renormalization group approach and scaling laws for the Lifshitz critical behavior

TL;DR

This paper introduces a novel renormalization group method to analyze Lifshitz critical behavior, deriving new scaling laws and fixed points for anisotropic and isotropic cases, advancing understanding of phase transitions.

Contribution

It presents a new RG approach for Lifshitz points, identifying independent fixed points and deriving generalized scaling laws for anisotropic and isotropic cases.

Findings

Identifies two independent fixed points for anisotropic Lifshitz points.

Derives new scaling laws extending previous results.

Separately describes isotropic case with a distinct fixed point.

Abstract

A new renormalization group treatment is proposed for the critical exponents of an m-fold Lifshitz point. The anisotropic cases (m not equal 8) are described by two independent fixed points associated to two independent momentum flow along the quadratic and quartic directions, respectively. The isotropic case is described separately. In that case, the fixed point is due to renormalization group transformations along the quartic directions. The new scaling laws are derived for both cases and generalize the ones previously reported.