m 轴 Lifshitz 点的大 n 展开
摘要
发展了关于 d 维系统在 m 轴 Lifshitz 点处临界行为的大 n 展开。推导了 O(1/n) 阶的两个独立关联指数 \eta_{L2} 和 \eta_{L4} 以及相关各向异性指数 \theta 的Leading non-trivial 贡献。这些 1/n 修正项的级数系数以积分形式给出，适用于一般的 m 和 d 值，满足 0<m<d 且 2+m/2<d<4+m/2。对于特定的 m 和 d 值，如 (m,d)=(1,4)，可解析计算，但一般需要数值方法。我们展示 1/n 修正项在适当极限下还原为已知的 d 维各向同性 Lifshitz 点和临界点的大 n 展开，同时符合关于上、下临界维数的可用维数展开。 presented for 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.
关键词
引用
@article{arxiv.cond-mat/0412405,
title = {Large-n expansion for m-axial Lifshitz points},
author = {M. A. Shpot and Yu. M. Pis'mak and H. W. Diehl},
journal= {arXiv preprint arXiv:cond-mat/0412405},
year = {2007}
}
备注
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