墙上方的$(2+1)$ D SOS曲面的形状
The shape of the $(2+1)$D SOS surface above a wall
摘要：
本文对Temperley（1952）提出的经典的（2+1）\Dim Solid-On-Solid模型的壁面形状作了全面的描述。在一个$L\times L$盒上，在一个大的逆温$β$下，对于大多数$L$值，大多数位点的高度集中在一个水平$h = \lfloor (1/4β)\log L\rfloor$上。对于一个发散的盒子序列的高度$(h,h-1,...)$水平线的合奏有一个Hausdorff距离的缩放限制当且仅当$(1/4β)\log L$的小数部分收敛到一个非临界值。缩放限制由通过平移Wulff形状形成的嵌套的不同循环明确给出。最后，$h$能级线的特征是来自侧边界的$L^{1/3+o(1)}$波动.
英文摘要：
We give a full description for the shape of the classical (2+1)\Dim Solid-On-Solid model above a wall, introduced by Temperley (1952). On an $L\times L$ box at a large inverse-temperature $β$ the height of most sites concentrates on a single level $h = \lfloor (1/4β)\log L\rfloor$ for most values of $L$. For a sequence of diverging boxes the ensemble of level lines of heights $(h,h-1,...)$ has a scaling limit in Hausdorff distance iff the fractional parts of $(1/4β)\log L$ converge to a noncritical value. The scaling limit is explicitly given by nested distinct loops formed via translates of Wulff shapes. Finally, the $h$-level lines feature $L^{1/3+o(1)}$ fluctuations from the side boundaries.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
