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Large-n expansion for m-axial Lifshitz points

M. A. Shpot·Yu. M. Pis'mak·H. W. Diehl
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Abstract

The large-n expansion is developed for the study of critical behaviour of d-dimensional systems at m-axial Lifshitz points with an arbitrary number m of modulation axes. The leading non-trivial contributions of O(1/n) are derived for the two independent correlation exponents η_{L2} and η_{L4}, and the related anisotropy index θ. The series coefficients of these 1/n corrections are given for general values of m and d with 0<m<d and 2+m/2<d<4+m/2 in the form of integrals. For special values of m and d such as (m,d)=(1,4), they can be computed analytically, but in general their evaluation requires numerical means. The 1/n corrections are shown to reduce in the appropriate limits to those of known large-n expansions for the case of d-dimensional isotropic Lifshitz points and critical points, respectively, and to be in conformity with available dimensionality expansions about the upper and lower critical dimensions. Numerical results for the 1/n coefficients of η_{L2}, η_{L4} and θare presented for the physically interesting case of a uniaxial Lifshitz point in three dimensions, as well as for some other choices of m and d. A universal coefficient associated with the energy-density pair correlation function is calculated to leading order in 1/n for general values of m and d.

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M. A. Shpot, Yu. M. Pis'mak, H. W. Diehl. 2005-01-21. Large-n expansion for m-axial Lifshitz points. https://doi.org/10.1088/0953-8984%2F17%2F20%2F020

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