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We investigate ground state configurations for a general finite number $N$ ofparticles of the Heitmann-Radin sticky disc pair potential model in twodimensions. Exact energy minimizers are shown to exhibit large microscopicfluctuations about the asymptotic Wulff shape which is a regular hexagon: Thereare arbitrarily large $N$ with ground state configurations deviating from thenearest regular hexagon by a number of $\sim N^{3/4}$ particles. We also provethat for any $N$ and any ground state configuration this deviation is boundedabove by $\sim N^{3/4}$. As a consequence we obtain an exact scaling law forthe fluctuations about the asymptotic Wulff shape. In particular, our resultsgive a sharp rate of convergence to the limiting Wulff shape.

Ground states of the 2D sticky disc model: fine properties and $N^{3/4}$ law for the deviation from the asymptotic Wulff shape