Critical, crossover and correction-to-scaling exponents for isotropic Lifshitz points to order (8 – d)²

A two-loop renormalization group analysis of the critical behaviour at an isotropic Lifshitz point is presented. Using dimensional regularization and minimal subtraction of poles, we obtain the expansions of the critical exponents ν and η, the crossover exponent φ, as well as the (related) wave vector exponent β_q and the correction-to-scaling exponent ω to second order in ₈ = 8 − d. They are compared with the authors' recent -expansion results (2000 Phys. Rev. B 62 12338, 2001 Nucl. Phys. B 612 340) for the general case of an m-axial Lifshitz point. It is shown that the expansions obtained here by a direct calculation for the isotropic (m = d) Lifshitz point all follow from the latter upon setting m = 8 − ₈. This is so despite recent claims to the contrary by de Albuquerque and Leite (2002 J. Phys. A: Math. Gen. 35 1807).