Spectrum and Completeness of the Integrable 3-state Potts Model: A Finite Size Study
Spectrum and Completeness of the Integrable 3-state Potts Model: A Finite Size Study
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可积三态 Potts 模型的谱和完整性：有限尺寸研究
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发表时间：
1992
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通讯作者：
B. McCoy
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作者：
G. Albertini;S. Dasmahapatra;B. McCoy
对于链长M≤7的可积三态Potts模型，其转移矩阵的所有本征值都以谱变量的多项式形式计算。零的本征值是已知的，以满足贝特的Anglomerate方程，因此它是特别感兴趣的是，我们发现许多解决方案的零不满足传统的“弦假设”。我们还发现，在许多情况下，整数的对数形式的贝特方程不满足单调性的性质，他们通常被假定为拥有。我们提出了一个分类的所有特征值的根的集合，并表明，对于所有M，这种分类产生一个完整的集合。
All eigenvalues of the transfer matrix of the integrable 3-state Potts model are computed as polynomials in the spectral variable for chains of length M≤7. The zeroes of the eigenvalues are known to satisfy a Bethe's Ansatz equation and thus it is of particular interest that we find many solutions whose zeroes do not satisfy the traditional "string hypothesis". We also find many cases where the integers in the logarithmic form of the Bethe equations do not satisfy the monotonicity properties that they are usually assumed to possess. We present a classification of all eigenvalues in terms of sets of roots and show that, for all M, this classification yields a complete set.