A combinatorial interpretation of the free-fermion condition of the six-vertex model
A combinatorial interpretation of the free-fermion condition of the six-vertex model
复制标题
六顶点模型自由费米子条件的组合解释
DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
A. Owczarek
中科院分区：
文献类型：
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作者：
R. Brak;A. Owczarek
六顶点模型的自由费米子条件提供了一个五参数子流形，在该子流形上，进入模型转移矩阵本征函数的波数的贝特假设方程解耦，从而允许得到显式解。这种条件最初出现在早期的场论S矩阵方法中。在这里，我们根据广义的盖塞尔 - 维耶诺对合为该条件提供了一种组合解释。通过这样做，我们将最初仅为无交叉路径设计的盖塞尔 - 维耶诺定理的应用扩展到一种特殊的加权交叉路径类型，从而根据单一路径的配分函数来表示在固定端点起始和终止的N条此类路径的配分函数。
The free-fermion condition of the six-vertex model provides a five-parameter sub- manifold on which the Bethe ansatz equations for the wavenumbers that enter into the eigenfunctions of the transfer matrices of the model decouple, hence allowing explicit solutions. Such conditions arose originally in early field-theoretic S-matrix approaches. Here we provide a combinatorial explanation for the condition in terms of a generalized Gessel-Viennot involution. By doing so we extend the use of the Gessel-Viennot theorem, originally devised for non-intersecting walks only, to a special weighted type of intersecting walk, and hence express the partition function of N such walks starting and finishing at fixed endpoints in terms of the single-walk partition functions.