经典海森堡自旋系统的基态理论I
Theory of ground states for classical Heisenberg spin systems I
摘要：
我们制定了一个严格的基态理论的经典，有限，海森堡自旋系统的第一部分。主要结果是所有的基态都可以由一个实对称矩阵的本征向量构造而成，该矩阵的元素包括自旋系统的耦合常数以及某些Lagrange参数。特征向量对应于最小特征值的唯一最大值，该最小特征值被认为是拉格朗日参数的函数。然而，有罕见的情况下，所有的基态以这种方式获得的非物理尺寸$M>3$和理论将不得不扩展。进一步的结果涉及的程度，额外的简并，额外的平凡简并的基态由于旋转或反射。用几个基本的例子来说明这个理论。
英文摘要：
We formulate part I of a rigorous theory of ground states for classical, finite, Heisenberg spin systems. The main result is that all ground states can be constructed from the eigenvectors of a real, symmetric matrix with entries comprising the coupling constants of the spin system as well as certain Lagrange parameters. The eigenvectors correspond to the unique maximum of the minimal eigenvalue considered as a function of the Lagrange parameters. However, there are rare cases where all ground states obtained in this way have unphysical dimensions $M>3$ and the theory would have to be extended. Further results concern the degree of additional degeneracy, additional to the trivial degeneracy of ground states due to rotations or reflections. The theory is illustrated by a couple of elementary examples.
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