二维粘盘模型基态的精细性质和偏离渐近Wulff形状的$N^{3/4}$定律
Ground states of the 2D sticky disc model: fine properties and $N^{3/4}$ law for the deviation from the asymptotic Wulff shape
摘要：
本文研究了二维Heitmann-Radin粘性盘对势模型中一般有限个$N$粒子的基态构型。精确的能量极小显示出大的微观波动的渐近武尔夫形状，这是一个正六边形：有任意大的$N$与基态配置偏离最近的正六边形由一些$\sim N^{3/4}$粒子。我们还证明了，对于任何$N$和任何基态配置，这种偏差是有界以上的$\sim N^{3/4}$。作为结果，我们得到一个精确的标度律的渐近伍尔夫形状的波动。特别是，我们的结果给出了一个尖锐的收敛速率的限制伍尔夫形状。
英文摘要：
We investigate ground state configurations for a general finite number $N$ of particles of the Heitmann-Radin sticky disc pair potential model in two dimensions. Exact energy minimizers are shown to exhibit large microscopic fluctuations about the asymptotic Wulff shape which is a regular hexagon: There are arbitrarily large $N$ with ground state configurations deviating from the nearest regular hexagon by a number of $\sim N^{3/4}$ particles. We also prove that for any $N$ and any ground state configuration this deviation is bounded above by $\sim N^{3/4}$. As a consequence we obtain an exact scaling law for the fluctuations about the asymptotic Wulff shape. In particular, our results give a sharp rate of convergence to the limiting Wulff shape.
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。
