Reply to "Comment on Renormalization group picture of the Lifshitz critical behaviors"

TL;DR

This paper defends a recently proposed approach to Lifshitz critical behavior against criticism, demonstrating its consistency and correctness in the ultraviolet regime through detailed theoretical arguments.

Contribution

It provides a rebuttal to prior criticism by showing the approach's consistency and validity at multiple loop levels in the renormalization group analysis.

Findings

The approach is free of inconsistencies in the ultraviolet regime.

The orthogonal approximation is consistent with homogeneity at arbitrary loop momenta.

The criticism by Diehl and Shpot is shown to be incorrect.

Abstract

We reply to a recent comment by Diehl and Shpot (cond-mat/0305131) criticizing a new approach to the Lifshitz critical behavior just presented (M. M. Leite Phys. Rev. B 67, 104415(2003)). We show that this approach is free of inconsistencies in the ultraviolet regime. We recall that the orthogonal approximation employed to solve arbitrary loop diagrams worked out at the criticized paper even at three-loop level is consistent with homogeneity for arbitrary loop momenta. We show that the criticism is incorrect.