论文标题
在六个Vertex模型的自由能
On the six-vertex model's free energy
论文作者
论文摘要
在本文中，我们提供了与六个vertex模型相关的Bethe Ansatz方程的存在的新证据和凝结，该模型具有周期性边界条件，并且在制度$Δ<1 $ <1 $中的六个Vertex方程和任意UP箭头（每行）的任意密度（每行）。作为应用程序，我们提供了六边形模型的自由能的简短，完全严格的计算，以及当上箭头的密度接近$ 1/2 $时，六佛特克斯分区函数的渐近扩展功能。后一个结果是在许多最新结果的基础上，尤其是随机群集模型的相位过渡的严格证明，当$ a = b = 1 $ a = 1 $ and $ c \ ge1 $以及六个vertex模型的旋转不变时，六个vertex高度函数的本地化/定位行为是六列vertex高度的本地化/定位行为的严格证明。
In this paper, we provide new proofs of the existence and the condensation of Bethe roots for the Bethe Ansatz equation associated with the six-vertex model with periodic boundary conditions and an arbitrary density of up arrows (per line) in the regime $Δ<1$. As an application, we provide a short, fully rigorous computation of the free energy of the six-vertex model on the torus, as well as an asymptotic expansion of the six-vertex partition functions when the density of up arrows approaches $1/2$. This latter result is at the base of a number of recent results, in particular the rigorous proof of continuity/discontinuity of the phase transition of the random-cluster model, the localization/delocalization behaviour of the six-vertex height function when $a=b=1$ and $c\ge1$, and the rotational invariance of the six-vertex model and the Fortuin-Kasteleyn percolation.
