Berlin 2005 – scientific programme
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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.