$N^2\times N^2$编织矩阵的多参数统计模型：所有$N$的传递矩阵${\bf T}^{(r)}$、自旋链、可因子分解散射的显式特征值
Multiparameter statistical models from $N^2\times N^2$ braid matrices: Explicit eigenvalues of transfer matrices ${\bf T}^{(r)}$, spin chains, factorizable scatterings for all $N$
摘要：
对于一类基于$N^2\times N^2$辫子矩阵的多参数统计模型，对所有$(r,N)$，显式地得到了传递矩阵${\bf T}^{(r)}$的特征值.我们的形式产生他们作为解决方案的线性方程组的简单常数系数。的零和多重构成的根的统一方面的作用被指出，其起源被追溯到循环排列的指数在我们的类的${\bf T}^{(r)}$矩阵诱导的基础状态的张量积。自由参数的作用，随着$N^2$和$N$的增加而增加，贯穿始终。对所有$N$构造并研究了自旋链哈密顿量.对于所有$N$，得到了辫子矩阵对应的Yang-Baxter矩阵的逆Cayley变换.它们为可因子分解的$S$ -矩阵提供了可能性。结论部分总结了研究的主要成果，并指出了研究的前景。
英文摘要：
For a class of multiparameter statistical models based on $N^2\times N^2$ braid matrices the eigenvalues of the transfer matrix ${\bf T}^{(r)}$ are obtained explicitly for all $(r,N)$. Our formalism yields them as solutions of sets of linear equations with simple constant coefficients. The role of zero-sum multiplets constituted in terms of roots of unity is pointed out and their origin is traced to circular permutations of the indices in the tensor products of basis states induced by our class of ${\bf T}^{(r)}$ matrices. The role of free parameters, increasing as $N^2$ with $N$, is emphasized throughout. Spin chain Hamiltonians are constructed and studied for all $N$. Inverse Cayley transforms of Yang-Baxter matrices corresponding to our braid matrices are obtained for all $N$. They provide potentials for factorizable $S$-matrices. Main results are summarized and perspectives are indicated in the concluding remarks.
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