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A two-loop renormalization group analysis of the critical behaviour at anisotropic Lifshitz point is presented. Using dimensional regularization andminimal subtraction of poles, we obtain the expansions of the criticalexponents $\nu$ and $\eta$, the crossover exponent $\phi$, as well as the(related) wave-vector exponent $\beta_q$, and the correction-to-scalingexponent $\omega$ to second order in $\epsilon_8=8-d$. These are compared withthe authors' recent $\epsilon$-expansion results [{\it Phys. Rev. B} {\bf 62}(2000) 12338; {\it Nucl. Phys. B} {\bf 612} (2001) 340] for the general case ofan $m$-axial Lifshitz point. It is shown that the expansions obtained here by adirect calculation for the isotropic ($m=d$) Lifshitz point all follow from thelatter upon setting $m=8-\epsilon_8$. This is so despite recent claims to thecontrary by de Albuquerque and Leite [{\it J. Phys. A} {\bf 35} (2002) 1807].Comment: 11 pages, Latex, uses iop stylefiles, some graphs are generated  automatically via texdra

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