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

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

2003-05-07

arxiv.org/abs/cond-mat/0305131v1

Phys.Rev. BD68 (2003) 066401; Phys.Rev. B67 (2003) 104415

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

10.1103/PhysRevB.68.066401

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

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