Transfer-matrix inverison identities for exactly solvable lattice-spin models.
Transfer-matrix inverison identities for exactly solvable lattice-spin models.
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精确可解晶格自旋模型的传递矩阵反演恒等式。
DOI：
10.1103/physrevlett.58.1502
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发表时间：
1987
影响因子：
8.6
通讯作者：
Pearce
中科院分区：
文献类型：
--
作者：
Pearce
针对八顶点模型，导出了一个新的行间交换矩阵所满足的函数方程。硬六边形、磁性硬正方形、自对偶Potts模型、Andrews-Baxter-Forrester模型等都满足相同形式的函数方程。这些新的函数方程被称为反演恒等式，因为它们推广了局部传递矩阵的反演关系。本文证明了所有满足Yang-Baxter方程的可解模型都具有这样的反演恒等式，并且一般来说，这些函数方程都可以解出传递矩阵的本征值。
A new functional equation satisfied by the commuting row-to-row transfer matrices is derived for the eight-vertex model. Functional equations of the same form are satisfied by hard hexagons, magnetic hard squares, the self-dual Potts models, the Andrews-Baxter-Forrester models, and others. These new functional equations are called inversion identities because they generalize the inversion relation for local transfer matrices. It is conjectured that all solvable models satisfying Yang-Baxter equations possess such inversion identities and that, in general, these functional equations can be solved for the transfer-matrix eigenvalues.