平面上的非临界局部高度概率与柱面上的临界配分函数
Off-critical local height probabilities on a plane and critical partition functions on a cylinder
摘要：
我们计算了在$4 N$ -象限螺旋几何结构中的第三种限制性固体-固体模型中的非临界局部高度概率，在角方向上具有周期性边界条件，在径向方向上具有固定边界条件，作为$N$，螺旋的缠绕数，和$τ$，偏离模型临界性的函数，并观察结果仅取决于产品$N \, τ$。在极限$N \rightarrow 1$，$τ\rightarrow τ_0$，使得$τ_0$是有限的，我们恢复了一个平面上的非临界局部高度概率，$τ_0$ -远离临界。在极限$N \rightarrow \infty$，$τ\rightarrow 0$中，使得$N \, τ= τ_0$是有限的，然后经过保角变换，我们得到了纵横比为$τ_0$的圆柱上的临界配分函数.我们的结论是，在一个平面上的非临界局部高度概率，$τ_0$ -远离临界，是等于一个临界配分函数上的纵横比$τ_0$，在协议Saleur和Bauer的结果。
英文摘要：
We compute off-critical local height probabilities in regime-III restricted solid-on-solid models in a $4 N$-quadrant spiral geometry, with periodic boundary conditions in the angular direction, and fixed boundary conditions in the radial direction, as a function of $N$, the winding number of the spiral, and $τ$, the departure from criticality of the model, and observe that the result depends only on the product $N \, τ$. In the limit $N \rightarrow 1$, $τ\rightarrow τ_0$, such that $τ_0$ is finite, we recover the off-critical local height probability on a plane, $τ_0$-away from criticality. In the limit $N \rightarrow \infty$, $τ\rightarrow 0$, such that $N \, τ= τ_0$ is finite, and following a conformal transformation, we obtain a critical partition function on a cylinder of aspect-ratio $τ_0$. We conclude that the off-critical local height probability on a plane, $τ_0$-away from criticality, is equal to a critical partition function on a cylinder of aspect-ratio $τ_0$, in agreement with a result of Saleur and Bauer.
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