论文标题
六个vertex模型的高度函数的离域化
Delocalization of the height function of the six-vertex model
论文作者
论文摘要
我们表明，在参数范围$ \ mathbf a = \ mathbf b = 1 $和$ \ mathbf c \ ge1 $中，六个vertex模型的高度函数在$ \ mathbf c \ le 2 $时将用对数方差定位。这补充了$ \ mathbf c> 2 $的较早验证的本地化。我们的证明依赖于Russo（Seymour） - Welsh型参数，以及圆柱六佛特尔斯模型的自由能的局部行为，这是向上和向下箭头数量之间不平衡的函数。
We show that the height function of the six-vertex model, in the parameter range $\mathbf a=\mathbf b=1$ and $\mathbf c\ge1$, is delocalized with logarithmic variance when $\mathbf c\le 2$. This complements the earlier proven localization for $\mathbf c>2$. Our proof relies on Russo--Seymour--Welsh type arguments, and on the local behaviour of the free energy of the cylindrical six-vertex model, as a function of the unbalance between the number of up and down arrows.
