Brenner型势的结晶
Crystallization for a Brenner-like potential
摘要：
石墨烯是一种具有蜂窝晶格结构的碳分子。我们展示了这种结构如何在二维中作为两体和三体项的相互作用能的最小值出现。在工程文献中，Brenner势通常用于描述碳原子之间的相互作用。我们考虑一个潜在的Stillinger-Weber型，它结合了某些特性的布伦纳潜力：首选的键角是180度，所有的相互作用有有限的范围。我们表明，每个粒子的基态能量的热力学极限是相同的蜂窝晶格。我们还证明了，受周期性边界条件，极小蜂窝晶格的翻译版本。
英文摘要：
Graphene is a carbon molecule with the structure of a honeycomb lattice. We show how this structure can arise in two dimensions as the minimizer of an interaction energy with two-body and three-body terms. In the engineering literature, the Brenner potential is commonly used to describe the interactions between carbon atoms. We consider a potential of Stillinger-Weber type that incorporates certain characteristics of the Brenner potential: the preferred bond angles are 180 degrees and all interactions have finite range. We show that the thermodynamic limit of the ground state energy per particle is the same as that of a honeycomb lattice. We also prove that, subject to periodic boundary conditions, the minimizers are translated versions of the honeycomb lattice.
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