论文标题
在磁盘的随机三角形上，顶点装饰的ISING模型中的接口
Interfaces in the vertex-decorated Ising model on random triangulations of the disk
论文作者
论文摘要
我们提供了一个框架，以研究Dobrushin边界条件在Ising模型的半平面版本上施加的界面，并在顶点上带有旋转的随机三角剖分。使用Albenque，Ménard和Schaeffer（[2]）的组合溶液以及Chen和Turunen（[8]，[9]）引入的生成函数方法，我们显示了磁盘的局部弱收敛性，如外膜趋向于无限性，并研究了dobrushin界面条件所用的界面。由于这项分析，我们验证了物理文献的启发式方法，这些物理文献的启发式方法是，高温方向上该模型的离散界面类似于关键位点渗透界面，并且在关键温度下提供了界面长度的显式缩放限制，这与恒定的liouville liou liouville liouville vastum量子vastitum量子量相吻合。总体而言，该模型比在面部上旋转的模型表现出更简单的结构，并证明了[8]，[9]中开发的方法的鲁棒性。
We provide a framework to study the interfaces imposed by Dobrushin boundary conditions on the half-plane version of the Ising model on random triangulations with spins on vertices. Using the combinatorial solution by Albenque, Ménard and Schaeffer ([2]) and the generating function methods introduced by Chen and Turunen ([8], [9]), we show the local weak convergence of such triangulations of the disk as the perimeter tends to infinity, and study the interface imposed by the Dobrushin boundary condition. As a consequence of this analysis, we verify the heuristics of physics literature that discrete interface of the model in the high-temperature regime resembles the critical site percolation interface, as well as provide an explicit scaling limit of the interface length at the critical temperature, which coincides with results on the continuum Liouville Quantum gravity surfaces. Overall, this model exhibits simpler structure than the model with spins on faces, as well as demonstrates the robustness of the methods developed in [8], [9].
