On the crystallization of 2D hexagonal lattices

E. Weinan, Dong Li

Research output: Contribution to journalArticlepeer-review

48 Scopus citations


It is a fundamental problem to understand why solids form crystals at zero temperature and how atomic interaction determines the particular crystal structure that a material selects. In this paper we focus on the zero temperature case and consider a class of atomic potentials V = V 2 + V 3, where V 2 is a pair potential of Lennard-Jones type and V 3 is a three-body potential of Stillinger-Weber type. For this class of potentials we prove that the ground state energy per particle converges to a finite value as the number of particles tends to infinity. This value is given by the corresponding value for a optimal hexagonal lattice, optimized with respect to the lattice spacing. Furthermore, under suitable periodic or Dirichlet boundary condition, we show that the minimizers do form a hexagonal lattice.

Original languageEnglish (US)
Pages (from-to)1099-1140
Number of pages42
JournalCommunications In Mathematical Physics
Issue number3
StatePublished - Mar 2009

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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