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DY: Dynamik und Statistische Physik

DY 23: Symposium Renormalization and Scaling (SYRS) – Contributed Talks I

DY 23.1: Talk

Saturday, March 5, 2005, 14:00–14:15, TU H3010

Large-n expansion for m-axial Lifshitz points — •Mykola Shpot¹, Yuri Pismak², and Hans Werner Diehl³ — ¹Institute for Condensed Matter Physics, 79011 Lviv, Ukraine — ²State University of Sankt-Petersburg, 198904 Sankt-Petersburg, Russia — ³Fachbereich Physik, Universität Duisburg-Essen, Campus Essen, D-45117 Essen, FRG

A large-n expansion is presented for m-axial Lifshitz points with an arbitrary number of anisotropy directions m in d dimensional space. The first non-trivial terms of order O(1/n) are derived for two independent correlation function critical exponents η₂ and η₄ and the related anisotropy index θ. Our results conform in appropriate limits with known large-n expansions for d-dimensional isotropic Lifshitz and critical points, as well as with available dimensionality expansions about the upper and lower critical dimensions. We give numerical values of the 1/n coefficients of η₂, η₄, and θ for physically most relevant case of uniaxial Lifshitz point in three dimensions, as well as for some other interesting choices of m and d. The O(1/n) terms of these exponents are derived in a closed form in the special case m=1, d=4.