Lifshitz-point critical behaviour to ${\boldsymbol{O(ε^2)}}$

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 $ε=4-d+\frac{m}{2}$ were presented for the critical exponents $ν_{\mathrm{L}2}$, $η_{\mathrm{L}2}$ and $γ_{\mathrm{L}2}$ 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.