Critical, crossover, and correction-to-scaling exponents for isotropic Lifshitz points to order $\boldsymbol{(8-d)^2}$

Details Critical, crossover, and correction-to-scaling exponents for isotropic Lifshitz points to order $\boldsymbol{(8-d)^2}$ Critical, crossover, and correction-to-scaling exponents for isotropic Lifshitz points to order $\boldsymbol{(8-d)^2}$

2002-04-12

arxiv.org/abs/cond-mat/0204267v1

J.Phys.A35:6249-6260,2002

Physics

Condensed Matter

Statistical Mechanics

11 pages, Latex, uses iop stylefiles, some graphs are generated automatically via texdraw

Scientific paper

10.1088/0305-4470/35/30/303

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 $\nu$ and $\eta$, the crossover exponent $\phi$, as well as the (related) wave-vector exponent $\beta_q$, and the correction-to-scaling exponent $\omega$ to second order in $\epsilon_8=8-d$. These are compared with the 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 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 $m=8-\epsilon_8$. This is so despite recent claims to the contrary by de Albuquerque and Leite [{\it J. Phys. A} {\bf 35} (2002) 1807].

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