A Note on the Eigenvalue Problem in Crystal Statistics.
A Note on the Eigenvalue Problem in Crystal Statistics.
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关于水晶统计中特征值问题的注释。
DOI：
10.1143/ptp/5.1.1
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发表时间：
1950
影响因子：
--
通讯作者：
Y. Nambu
中科院分区：
文献类型：
--
作者：
Y. Nambu
有序无序转变的数学理论几位作者发现了确定具有简单相互作用模型的格点的配分函数的问题。将其简化为一个本征值问题，该问题更容易处理，并且，通过适当的近似，将比以前的理论揭示更精细的相变细节。这种攻击方法在Onsager的工作中达到了顶峰，2）他成功地给出了二维简单正方形伊辛格的上述本征值问题的严格解。然而，所涉及的数学工具是如此复杂，以至于人们在超复数的丛林中会完全失去视线。Husimi和Syozi3）在这一数学点上取得了相当大的改进，他们用它来解决蜂窝型晶格的本征值问题。本作者，独立于他们，“已经达到或多或少类似的想法和考虑。本文拟对此作简要的论述。虽然到目前为止还没有尝试过大量的应用，也没有任何物理上的新东西，但可以希望它会为那些对这些问题感兴趣的人带来一些好处。
mathematical theory of order-disorder transition. The problem of determining the partition function for a lattice with simple interaction model was found, by severai authors,!) to be reduced to an eigenvalue problem which is easier to handle with,and which, with suitable approximations, would reveal more refined details of the phase transition than the former theories. This method of attack culminated in the work of Onsager,2) who succeeded In giving the rigorous solution of the above mentioned eigenvalue problem for two-dimensional simple square Ising lattice. The mathematical tools involved, however, are so hopelessly complicated that one would quite simply lose sight in the jungle of hypercomplex numbers. A con siderable improvement on this mathematical point has been attainp.d by Husimi and Syozi3) who used it to solve the eigenvalue problem for the honeycomb type lattice. The present author, independently of them,' has reached more or less similar ideas and considerations. which it is the purpos~ of the present paper to expose in brief detail. Though as yet no substantial applications has been attempted, nor anything physically new has been derived, it may be hoped that it will do some profit for those who are interested in such problems.