2004/12/31 by M. A. Shpot, Yu. M. Pis'mak, H. W. Diehl
Physics and Astronomy · #cond-mat.stat-mech #hep-th
paper · pdf · doi:10.1088/0953-8984/17/20/020
published as J.Phys.Condens.Matter 17 (2005) S1947-S1972 · 28 pages, 3 figures. Submitted to: J. Phys. C: Solid State Phys., special issue dedicated to Lothar Schaefer on the occasion of his 60th birthday. V2: References added along with corresponding modifications in the text, corrected figure 3, corrected typos
arxiv created 2005/01/21 · arxiv updated 2009/12/01
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 ηL2 and ηL4, 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 ηL2, ηL4 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.