各向异性三角格子上Ising模型的对角两点关联和Garnier系统
The diagonal two-point correlations of the Ising model on the anisotropic triangular lattice and Garnier systems
摘要：
利用第六类Painlevé系统的三变量扩展即Garnier系统的解，计算了三个方向上具有一般耦合的三角晶格上Ising模型的对角自旋-自旋关联$ \langle σ_{0,0}σ_{N,N} \rangle $.这种识别，这是使用双正交多项式的理论与正规半经典的权重单位圆上完成的，有一个额外的后果，其中的相关性的特点是一个简单的系统的耦合，非线性递归关系的自旋分离$ N \in \mathbb{Z}_{\geq 0} $。这些后来的递归关系是离散卡尼尔方程的一个例子，而卡尼尔方程又是“离散Painlevé V”系统的扩展。
英文摘要：
The diagonal spin-spin correlations $ \langle σ_{0,0}σ_{N,N} \rangle $ of the Ising model on a triangular lattice with general couplings in the three directions are evaluated in terms of a solution to a three-variable extension of the sixth Painlevé system, namely a Garnier system. This identification, which is accomplished using the theory of bi-orthogonal polynomials on the unit circle with regular semi-classical weights, has an additional consequence whereby the correlations are characterised by a simple system of coupled, nonlinear recurrence relations in the spin separation $ N \in \mathbb{Z}_{\geq 0} $. These later recurrence relations are an example of the discrete Garnier equations which, in turn, are extensions to the "discrete Painlevé V" system.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
