论文标题
关于六个Vertex模型中的DELEPAILIZER
On delocalization in the six-vertex model
论文作者
论文摘要
我们表明，随着圆环的大小增长到无限，在[\ sqrt 3，2] $中具有参数$ c \ in [\ sqrt 3，2] $的六个vertex模型具有巨大的无限量限制。此外，我们证明，对于$ c \在[\ sqrt {2+ \ sqrt 2}，2] $中，$ \ mathbb z^2 $上关联的高度函数具有无绑定的差异。 证明依赖于六vertex模型的百特 - 凯兰德 - WU表示的扩展，以对相关旋转模型的多点相关函数。其他关键成分是[1,4] $中$ q \的关键随机群集度量的唯一性和渗透特性，以及最新的结果，将自旋模型中相关性的衰减与高度函数的离域化有关。
We show that the six-vertex model with parameter $c\in[\sqrt 3, 2]$ on a square lattice torus has an ergodic infinite-volume limit as the size of the torus grows to infinity. Moreover we prove that for $c\in[\sqrt{2+\sqrt 2}, 2]$, the associated height function on $\mathbb Z^2$ has unbounded variance. The proof relies on an extension of the Baxter-Kelland-Wu representation of the six-vertex model to multi-point correlation functions of the associated spin model. Other crucial ingredients are the uniqueness and percolation properties of the critical random cluster measure for $q\in[1,4]$, and recent results relating the decay of correlations in the spin model with the delocalization of the height function.
