论文标题
关键平面晶格模型中的旋转不变性
Rotational invariance in critical planar lattice models
论文作者
论文摘要
在本文中，我们证明许多二维晶格模型的大规模特性在旋转上不变。更确切地说，我们证明了带有集群权威$ 1 \ le le q \ le 4 $的正方形晶格上的随机群集模型在大尺度上展示旋转不变性。这涵盖了在方格上伯努利渗透的情况，这是一个重要的例子。我们从这个结果中推断出Potts模型与$ q \ in \ {2,3,4 \} $颜色的相关性和六列vertex高度功能的$δ\在[-1，-1/2] $ in [-1，-1/2] $ in [-1，-1/2] $在大尺度上都是旋转不变的。
In this paper, we prove that the large scale properties of a number of two-dimensional lattice models are rotationally invariant. More precisely, we prove that the random-cluster model on the square lattice with cluster-weight $1\le q\le 4$ exhibits rotational invariance at large scales. This covers the case of Bernoulli percolation on the square lattice as an important example. We deduce from this result that the correlations of the Potts models with $q\in\{2,3,4\}$ colors and of the six-vertex height function with $Δ\in[-1,-1/2]$ are rotationally invariant at large scales.
