Isotropic Lifshitz critical behavior from the functional renormalization group

TL;DR

This paper investigates the isotropic Lifshitz critical behavior in a single component field theory using the Functional Renormalization Group, identifying fixed points in specific spatial dimensions through advanced flow equation analysis.

Contribution

It provides new insights into Lifshitz fixed points by applying the Functional Renormalization Group with a Proper Time regulator at various orders of the derivative expansion.

Findings

Fixed point solutions exist for 5.5 < d < 8

Analysis at lowest and higher order in derivative expansion

Use of Proper Time regulator in flow equations

Abstract

The Lifshitz critical behavior for a single component field theory is studied for the specific isotropic case in the framework of the Functional Renormalization Group. Lifshitz fixed point solutions of the flow equation, derived by using a Proper Time regulator, are searched at lowest and higher order in the derivative expansion. Solutions are found when the number of spatial dimensions d is contained within the interval 5.5 < d < 8.