# Isotropic Lifshitz point in the O(N) Theory

## TL;DR

This paper investigates the existence and properties of an isotropic Lifshitz point in the O(N) scalar theory using the 1/N expansion and Functional Renormalization Group methods, revealing its dimensional range and critical exponents.

## Contribution

It provides a detailed analysis of the isotropic Lifshitz point in the O(N) theory, including eigenvalue spectra and anomalous dimensions at leading and next-to-leading orders.

## Key findings

- Lifshitz point exists for dimensions between 4 and 8.
- Anomalous dimension eta_N vanishes at d=4 and d=8.
- Eta_N is positive between these dimensions, depending on the regulator.

## Abstract

The presence of an isotropic tricritical Lifshitz point for the O(N) scalar theory is investigated in the 1/N expansion by means of the Functional Renormalization Group equations. At leading order, the non-trivial Lifshitz point is observed if the number of dimensions d is taken between d=4 and d=8, and the eigenvalue spectrum of the associated eigendirections is derived. At order 1/N, the anomalous dimension eta_N is computed and it is found to vanish both in d=4 and d=8, while it turns out to be positive between these two values, although strongly dependent on the choice of infrared regulator.