Lifshitz-point correlation length exponents from the large-n expansion

Abstract

The large-n expansion is applied to the calculation of thermal critical exponents describing the critical behavior of spatially anisotropic d-dimensional systems at m-axial Lifshitz points. We derive the leading nontrivial 1/n correction for the perpendicular correlation-length exponent nu_{L2} and hence several related thermal exponents to order O(1/n). The results are consistent with known large-n expansions for d-dimensional critical points and isotropic Lifshitz points, as well as with the second-order epsilon expansion about the upper critical dimension d^*=4+m/2 for generic m\in[0,d]. Analytical results are given for the special case d=4, m=1. For uniaxial Lifshitz points in three dimensions, 1/n coefficients are calculated numerically. The estimates of critical exponents at d=3, m=1 and n=3 are discussed.

27 pages, submitted to Nucl. Phys. B. V2 - journal version with an extended introduction containing a short review of both Lifshitz-point and Lorentz-violating theories

References in corpus (20)

• Quantum Gravity at a Lifshitz Point
• Membranes at Quantum Criticality
• Phenomenologically viable Lorentz-violating quantum gravity
• Lorentz symmetry breaking as a quantum field theory regulator
• Cosmology of the Lifshitz universe
• Renormalization of Lorentz violating theories
• Renormalization group in Lifshitz-type theories
• Weighted power counting and Lorentz violating gauge theories. I: General properties
• General Covariance in Gravity at a Lifshitz Point
• Weighted power counting and Lorentz violating gauge theories. II: Classification
• Renormalization of Scalar and Yukawa Field Theories with Lorentz Violation
• Weighted power counting, neutrino masses and Lorentz violating extensions of the Standard Model
• Status of Horava gravity: A personal perspective
• Diversity of critical behavior within a universality class
• Fluctuation-induced forces in strongly anisotropic critical systems
• Dynamic critical behavior of model A in films: Zero-mode boundary conditions and expansion near four dimensions
• Large-n expansion for m-axial Lifshitz points
• Lifshitz scalar fields: one loop renormalization in curved backgrounds
• Relevance of space anisotropy in the critical behavior of m-axial Lifshitz points
• Compatibility of 1/n and epsilon expansions for critical exponents at m-axial Lifshitz points

Cited by in corpus (7)

• Higher order singletons, partially massless fields and their boundary values in the ambient approach
• Quantum phase transition in the spin-anisotropic quantum spherical model
• The Clausenian hypergeometric function ${}_3{F}_2$ with unit argument and negative integral parameter differences
• Stability of the Fulde-Ferrell-Larkin-Ovchinnikov states in anisotropic systems and critical behavior at thermal $m$-axial Lifshitz points
• A Feynman integral in Lifshitz-point and Lorentz-violating theories in $R^D\oplus R^m$
• Dynamic critical exponent in quantum long-range models
• Feynman integral in ${\mathbb{R}}^1\oplus {\mathbb{R}}^m$ and complex expansion of ${}_2{F}_1$