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

Abstract

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.

REVTeX 4, 22 pages

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• Susceptibility amplitude ratio for generic competing systems
• Universality hypothesis breakdown at one-loop order
• Asymptotic single-particle states and exact Lorentz-violating all-loop quantum corrections for scalar field theory
• Emergent gauge bosons and dynamical symmetry breaking in a four-fermion Lifshitz model
• Unconventional minimal subtraction and Callan-Symanzik methods for Lorentz-violating scalar field theories at all loop orders
• Probing the two-scale-factor universality hypothesis by exact rotation symmetry-breaking mechanism