Comment on “Renormalization-group picture of the Lifshitz critical behavior”

We show that the recent renormalization-group analysis of Lifshitz critical behavior presented by Leite [Phys. Rev. B 67, 104415 (2003)] suffers from a number of severe deficiencies. In particular, we show that his approach does not give an ultraviolet finite renormalized theory, is plagued by inconsistencies, misses the existence of a nontrivial anisotropy exponent $\theta \ne 1/2,$ and therefore yields incorrect hyperscaling relations. His $\epsilon$-expansion results to order ${\epsilon }^2$ for the critical exponents of m-axial Lifshitz points are incorrect in both the anisotropic $\mathrm{}(0<m<d)\mathrm{}$ and isotropic $\mathrm{}(m=d)\mathrm{}$ cases. The inherent inconsistencies and the lack of a sound basis of the approach makes its results unacceptable even if they are interpreted in the sense of approximations.