Callan-Symanzik method for $m$-axial Lifshitz points

Details Callan-Symanzik method for $m$-axial Lifshitz points Callan-Symanzik method for $m$-axial Lifshitz points

2007-04-24

arxiv.org/abs/0704.3208v1

Annals Phys.324:178-204,2009; Erratum-ibid.324:2452,2009

Physics

High Energy Physics

High Energy Physics - Theory

REVTeX 4, 22 pages

Scientific paper

10.1016/j.aop.2008.05.006 10.101

We introduce the Callan-Symanzik method in the description of anisotropic as well as isotropic Lifshitz critical behaviors. Renormalized perturbation theories are defined by normalization conditions with nonvanishing masses and at zero external momenta. The orthogonal approximation is employed to obtain the critical indices $\eta_{L2}$, $\nu_{L2}$, $\eta_{L4}$ and $\nu_{L4}$ diagramatically at least up to two-loop order in the anisotropic criticalities. This approximation is also utilized to compute the exponents $\eta_{L4}$ and $\nu_{L4}$ in the isotropic case. Furthermore, we compute those exponents exactly for the isotropic behaviors at the same loop order. The results obtained for all exponents are in perfect agreement with those previously derived in the massless theories renormalized at nonzero external momenta.

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