Comment on ``Renormalization-group picture of the Lifshitz critical behavior''

Abstract

We show that the recent renormalization-group analysis of Lifshitz critical behavior presented by Leite [Phys. Rev. B {\bf 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 both in the anisotropic ($0<m<d$) and the isotropic cases ($m=d$). 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.

arXiv commentA comment on M. Leite, Phys Rev B 67, 104415 (2003) revtex4, 2 pages

References in corpus (6)

• Critical behavior at m-axial Lifshitz points: field-theory analysis and $\epsilon$-expansion results
• Two-loop renormalization-group analysis of critical behavior at m-axial Lifshitz points
• A new picture of the Lifshitz critical behavior
• Critical, crossover, and correction-to-scaling exponents for isotropic Lifshitz points to order $(8-\mathbf{d}{)}^2$
• Anisotropic Lifshitz Point at $O({\epsilon }_L^2)$
• Lifshitz-point critical behaviour to $\mathbf{O}({\mathbf{\epsilon }}^2)$

Cited by in corpus (7)

• Large-n expansion for m-axial Lifshitz points
• Relevance of space anisotropy in the critical behavior of m-axial Lifshitz points
• Specific heat amplitude ratios for anisotropic Lifshitz critical behaviors
• Bulk and Boundary Critical Behavior at Lifshitz Points
• Multicriticality of the (2+1)-dimensional gonihedric model: A realization of the (d,m)=(3,2) Lifshitz point
• A Feynman integral in Lifshitz-point and Lorentz-violating theories in $R^D\oplus R^m$
• Reply to "Comment on Renormalization group picture of the Lifshitz critical behaviors"