Loops statistics in the toroidal honeycomb dimer model
Loops statistics in the toroidal honeycomb dimer model
复制标题
环形蜂窝二聚体模型中的循环统计
DOI：
10.1214/09-aop453
复制
发表时间：
2006
影响因子：
4.5
通讯作者：
B. Tilière
中科院分区：
文献类型：
--
作者：
Cédric Boutillier;B. Tilière
嵌入环面的图形上的二聚体模型可以解释为随机自回避循环的集合。本文考虑均匀环形蜂窝状二聚体模型。证明了当图的网格趋于零且环面长固定时，环路集合的圈数规律收敛于二维离散高斯分布。对于物理学家来说，从他们对环面二维临界环模型的分析及其对环面上无质量自由场的映射中可以更普遍地了解到这一点。本文在环面二聚体模型引起的环模型的特殊情况下，首次用数学证明了这一更一般的物理结果。
The dimer model on a graph embedded in the torus can be interpreted as a collection of random self-avoiding loops. In this paper, we consider the uniform toroidal honeycomb dimer model. We prove that when the mesh of the graph tends to zero and the aspect of the torus is fixed, the winding number of the collection of loops converges in law to a two-dimensional discrete Gaussian distribution. This is known to physicists in more generality from their analysis of toroidal two-dimensional critical loop models and their mapping to the massless free field on the torus. This paper contains the first mathematical proof of this more general physics result in the specific case of the loop model induced by a toroidal dimer model.