Abstract

The Kramers–Wannier transfer matrix method is generalized to an arbitrary decoration number of the Ising chain. An exact analytical expression is obtained for the largest eigenvalue of the transfer matrix of a decorated Ising chain in the presence of an external magnetic field. Frustration points and the values of frustration magnetic fields are found that depend on the magnitudes and signs of exchange interactions. Exact expressions are obtained for zero-temperature entropies and zero-temperature magnetizations of the model under consideration. Magnetic phase diagrams of the ground state of the system are constructed for decoration values of d = 1 and d = 2, including those in the absence of a magnetic field. A comparison is made with a decorated square lattice not only in the absence but also in the presence of a magnetic field.

中文翻译：

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在磁场中装饰的伊辛链

摘要

Kramers-Wannier转移矩阵方法可以推广到Ising链的任意装饰数。在存在外部磁场的情况下，可以获得经过修饰的伊辛链转移矩阵的最大特征值的精确解析表达式。发现挫折点和挫折磁场的值取决于交换相互作用的大小和符号。获得了所考虑模型的零温度熵和零温度磁化强度的精确表达式。针对d = 1和d的装饰值构造系统基态的磁相图= 2，包括那些没有磁场的磁场。不仅在不存在磁场的情况下，而且在存在磁场的情况下，都与装饰的方格进行比较。