Lifshitz-point correlation length exponents from the large-n expansion Original Research Article

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 non-trivial image correction for the perpendicular correlation-length exponent image and hence several related thermal exponents to order image. 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 image for generic image. Analytical results are given for the special case image, image. For uniaxial Lifshitz points in three dimensions, image coefficients are calculated numerically. The estimates of critical exponents at image, image and image are discussed.