We study an infinite one-dimensional Ising spin chain where each particle interacts only with its nearest neighbors and is in contact with a heat bath with temperature decaying hyperbolically along the chain. The time evolution of the magnetization (spin expectation value) is governed by a semi-infinite Jacobi matrix. The matrix belongs to a three-parameter family of Jacobi matrices whose spectral problem turns out to be solvable in terms of the basic hypergeometric series. As a consequence, we deduce the essential properties of the corresponding orthogonal polynomials, which seem to be new. Finally, we return to the Ising model and study the time evolution of magnetization and two-spin correlations.

中文翻译：

---

新的对称正交多项式族和动力学自旋链的可解模型

我们研究无限一维 Ising 自旋链，其中每个粒子仅与其最近的邻居相互作用，并且与温度沿链双曲线衰减的热浴接触。磁化强度的时间演变（自旋期望值）由半无限雅可比矩阵控制。该矩阵属于雅可比矩阵的三参数族，其谱问题可以根据基本超几何级数解决。因此，我们推导出相应正交多项式的基本性质，这似乎是新的。最后，我们回到 Ising 模型并研究磁化强度和双自旋相关性的时间演化。