论文标题
二维无限海森堡古典方晶格：零场分区和相关长度
The two-dimensional infinite Heisenberg classical square lattice: zero-field partition function and correlation length
论文作者
论文摘要
我们严格检查了由最初最邻居之间耦合的各向同性的经典旋转组成的2D平方晶格。对于任何晶格大小，都建立了与零场分区函数ZINF {N}（0）相关的特征多项式的一般表达。在无限晶格限制中，数值研究允许选择主要术语：将其写成特征值的L系列，每个词都以独特的索引l为特征，其起源被解释了。出乎意料的是，Zinf {n}（0）显示了一个非常简单的精确闭合形式表达式，适用于任何温度。基本L期限的热研究允许指出L-和（L+1）–Term之间的交叉。来自L = 0-任期占主导地位的高温，越来越多地选择了L-EIGENVALUES的L-EIGENVALUE。在t = 0 k l倾向于无穷大，所有连续的主要l-eigenvalues等效。由于z旋转相关性的无效T大于0 k，但等于t = 0 k的1（绝对值），临界温度为tinf {c} = 0 k。使用与ZINF {n}（N}（0）使用的分析方法相似的分析方法，我们还提供了适用于Spin-Spin相关温度的确切表达式，适用于Spin-Spin相关的任何温度。在t = 0限制中，我们获得了一个磁相图，该图与通过重新规定方法得出的磁相图。通过取下XSI的低温极限，我们获得了与通过重新规定过程得出的相应表达式相同的表达式，对于磁相图的每个区域，因此首次使模型的完整精确解对任何温度有效。
We rigorously examine 2d-square lattices composed of classical spins isotropically coupled between first-nearest neighbours. A general expression of the characteristic polynomial associated with the zero-field partition function Zinf{N}(0) is established for any lattice size. In the infinite-lattice limit a numerical study allows to select the dominant term: it is written as a l-series of eigenvalues, each one being characterized by a unique index l whose origin is explained. Surprisingly Zinf{N}(0) shows a very simple exact closed-form expression valid for any temperature. The thermal study of the basic l-term allows to point out crossovers between l- and (l+1)-terms. Coming from high temperatures where the l=0-term is dominant and going to 0 K, l-eigenvalues showing increasing l-values are more and more selected. At T = 0 K l tends to infinity and all the successive dominant l-eigenvalues become equivalent. As the z-spin correlation is null for T greater than 0 K but equal to 1 (in absolute value) for T = 0 K the critical temperature is Tinf{c} = 0 K. Using an analytical method similar to the one employed for Zinf{N}(0) we also give an exact expression valid for any temperature for the spin-spin correlations as well as for the correlation length xsi. In the T=0-limit we obtain a diagram of magnetic phases which is similar to the one derived through a renormalization approach. By taking the low-temperature limit of xsi we obtain the same expressions as the corresponding ones derived through a renormalization process, for each zone of the magnetic phase diagram, thus bringing for the first time a strong validation to the full exact solution of the model valid for any temperature.
