双周期 Aztec 钻石的完美 t-嵌入

我们研究了来源于具有周期边权的 Aztec 钻石上的二面模型所产生的 t-表面——成对完美 t-嵌入及其相关的 origami 图——的大尺度几何。我们证明了这些 t-表面收敛于米氏空间 $\mathbb{R}^{2,2}$ 中的时光最大表面。我们观察到冻结区和气体区对限制表面几何产生显著影响：所有冻结区坍缩到四个边界点， regardless of the number of frozen regions, while each gas region collapses to a distinct light-like cusp in the interior of the surface. In the absence of gas regions, the limiting surface lies entirely within $\mathbb{R}^{2,1}$; in the general case, however, this is no longer true. The limiting surface is sensitive to the detailed structure of the model: both the positions of the cusps, and the placement of the boundary vertices, depend on the precise way the edge weights are distributed on the Aztec diamond. Nevertheless, we show that the global conformal structure remains robust and coincides with the Kenyon-Okounkov conformal structure. We further conjecture that the cusp locations encode the shift in the discrete Gaussian component that appears in the global fluctuations of the dimer model.