Reply on "Lifshitz-point critical behaviour to $O({\epsilon }_L^2)$"

Abstract

We reply to a recent comment by H. W. Diehl and M. Shpot (cond-mat/0106502) criticizing our paper J. Phys. A: Math. Gen. 34 (2001) L327-332. We show that the approximation we use for evaluating higher-loop integrals is consistent with homogeneity. A new renormalization group approach is presented in order to compare the two methods with high-precision numerical data concerning the uniaxial case. We stress that the isotropic behaviour cannot be obtained from the anisotropic one.

Minor modifications according to the referee's suggestions

References in corpus (5)

• Aging, phase ordering and conformal invariance
• Two-loop renormalization-group analysis of critical behavior at m-axial Lifshitz points
• Anisotropic scaling and generalized conformal invariance at Lifshitz points
• Anisotropic Lifshitz Point at $O({\epsilon }_L^2)$
• Lifshitz-point critical behaviour to $\mathbf{O}({\mathbf{\epsilon }}^2)$

Cited by in corpus (5)

• Phenomenology of local scale invariance: from conformal invariance to dynamical scaling
• A new picture of the Lifshitz critical behavior
• Critical, crossover, and correction-to-scaling exponents for isotropic Lifshitz points to order $(8-\mathbf{d}{)}^2$
• New universality classes for generic higher character Lifshitz points
• Reply to "Comment on Renormalization group picture of the Lifshitz critical behaviors"