Isotropic Lifshitz Scaling in four dimensions

TL;DR

This paper investigates isotropic Lifshitz points in four-dimensional O(N) scalar theories using the Functional Renormalization Group, revealing a line of fixed points in the O(2) case similar to the BKT phase.

Contribution

It provides evidence for a continuous line of fixed points at the lower critical dimension in four-dimensional Lifshitz theories, highlighting a novel phase structure.

Findings

Line of fixed points for O(2) theory at d=4

Similarity to Berezinskii-Kosterlitz-Thouless phase

Potential new phase transition in Lifshitz theories

Abstract

The presence of isotropic Lifshitz points for a O(N)-symmetric scalar theory is investigated with the help of the Functional Renormalization Group. In particular, at the supposed lower critical dimension d=4, evidence for a continuous line of fixed points is found for the O(2) theory, and the observed structure presents clear similarities with the properties observed in the 2-dimensional Berezinskii-Kosterlitz-Thouless phase.