Isotropic Lifshitz point in the O (N) theory

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 dis taken between d = 4and d = 8, and the eigenvalue spectrum of the associated eigendirections is derived. At order 1/N of the LPA' the anomalous dimension eta N is computed and it is found to vanish both in d = 4and d = 8. The dependence of our findings on the infrared regulator is discussed. (C) 2017 The Author. Published by Elsevier B.V.