Lifshitz-point critical behaviour to $\mathbf{O}({\mathbf{\epsilon }}^2)$

Abstract

We comment on a recent letter by L. C. de Albuquerque and M. M. Leite (J. Phys. A: Math. Gen. 34 (2001) L327-L332), in which results to second order in $\epsilon =4-d+\frac{m}{2}$ were presented for the critical exponents ${\nu }_{\mathrm{L}2}$, ${\eta }_{\mathrm{L}2}$ and ${\gamma }_{\mathrm{L}2}$ of d-dimensional systems at m-axial Lifshitz points. We point out that their results are at variance with ours. The discrepancy is due to their incorrect computation of momentum-space integrals. Their speculation that the field-theoretic renormalization group approach, if performed in position space, might give results different from when it is performed in momentum space is refuted.

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References in corpus (2)

• Two-loop renormalization-group analysis of critical behavior at m-axial Lifshitz points
• Anisotropic Lifshitz Point at $O({\epsilon }_L^2)$

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