Given a finite rhombus tiling of a polygonal region in the plane, the associated critical Z-invariant Ising model is invariant under star-triangle transformations. We give a simple matrix formula describing spin correlations between boundary vertices in terms of the shape of the region. When the region is a regular polygon, our formula becomes an explicit trigonometric sum.

中文翻译：

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临界 Ising 模型的边界相关公式

给定平面中多边形区域的有限菱形平铺，相关的临界Z不变 Ising 模型在星三角变换下是不变的。我们给出了一个简单的矩阵公式来描述边界顶点之间根据区域形状的自旋相关性。当该区域是一个正多边形时，我们的公式就变成了一个显式的三角和。