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 ∼N3/4 particles. We also prove
that for any N and any ground state configuration this deviation is bounded
above by ∼N3/4. 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