具有各向异性竞争作用的XY模型的（m，d，N）=（1，3，2）Lifshitz点和三维XY普适类的高温二元序列研究
A study of the (m,d,N)=(1,3,2) Lifshitz point and of the three- dimensional XY universality class by high-temperature bivariate series for the XY models with anisotropic competing interactions
摘要：
高温双变量展开已被推导出的两个自旋相关函数在各种经典的晶格XY（平面旋转器）模型中，其中空间各向同性的相互作用之间的第一个邻居的自旋竞争空间各向同性或各向异性（特别是单轴）之间的相互作用最近的邻居的自旋。对d= 1，2和3维立方晶格计算的展开式用两个变量K1=J1/kT和K2=J2/kT表示，其中J1和J2分别是最近邻和次近邻交换耦合。本报告特别讨论d=3单轴XY模型（ANNNXY模型）的性质，它的二元展开式已计算到第18阶，从而将迄今为止得到的结果扩展了12阶，并使在竞争参数R=J2/J1的广泛范围内对该模型进行研究成为可能。
英文摘要：
High-temperature bivariate expansions have been derived for the two-spin correlation-function in a variety of classical lattice XY (planar rotator) models in which spatially isotropic interactions among first-neighbor spins compete with spatially isotropic or anisotropic (in particular uniaxial) interactions among next-to-nearest-neighbor spins. The expansions, calculated for cubic lattices of dimension d=1,2 and 3, are expressed in terms of the two variables K1=J1/kT and K2=J2/kT, where J1 and J2 are the nearest-neighbor and the next-to-nearest-neighbor exchange couplings, respectively. This report deals in particular with the properties of the d=3 uniaxial XY model (ANNNXY model) for which the bivariate expansions have been computed through the 18-th order, thus extending by 12 orders the results so far available and making a study of this model possible over a wide range of values of the competition parameter R=J2/J1.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
