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 \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.