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Ground states of the 2D sticky disc model: fine properties and $$N^{3/4}$$ law for the deviation from the asymptotic Wulff shape. (English) Zbl 1292.82027
Summary: 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.
Reviewer: Reviewer (Berlin)

##### MSC:
 82C22 Interacting particle systems in time-dependent statistical mechanics
##### Keywords:
atomistic systems; Wulff shape; surface fluctuations
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##### References:
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