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

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dc.creatorDiehl, H. W.
dc.creatorShpot, M.
dc.date2002-04-12
dc.date.accessioned2026-07-07T10:48:05Z
dc.date.available2026-07-07T10:48:05Z
dc.descriptionA 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 $ε_8=8-d$. These are compared with the authors' recent $ε$-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 $m=8-ε_8$. This is so despite recent claims to the contrary by de Albuquerque and Leite [{\it J. Phys. A} {\bf 35} (2002) 1807].
dc.description11 pages, Latex, uses iop stylefiles, some graphs are generated automatically via texdraw
dc.identifierhttps://arxiv.org/abs/cond-mat/0204267
dc.identifierhttp://arxiv.org/abs/cond-mat/0204267
dc.identifierJ.Phys.A35:6249-6260,2002
dc.identifierdoi:10.1088/0305-4470/35/30/303
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/183754
dc.subjectStatistical Mechanics
dc.subjectSoft Condensed Matter
dc.subjectHigh Energy Physics - Theory
dc.titleCritical, crossover, and correction-to-scaling exponents for isotropic Lifshitz points to order $\boldsymbol{(8-d)^2}$
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