Isotropic Lifshitz point in the O(N) theory

Abstract

The presence of an isotropic tricritical Lifshitz point for the O(N) scalar theory is investigated at large N in the improved Local Potential Approximation (LPA′) 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 of the LPA′ the anomalous dimension ηN is computed and it is found to vanish both in d=4 and d=8. The dependence of our findings on the infrared regulator is discussed. Keywords: Functional Renormalization Group, Lifshitz point, 1/N expansion