A Proof of Finite Crystallization via Stratification

Friedrich M, Kreutz L (2023)

Publication Type: Journal article

Publication year: 2023


Book Volume: 190

Article Number: 199

Journal Issue: 12

DOI: 10.1007/s10955-023-03202-7


We devise a new technique to prove two-dimensional crystallization results in the square lattice for finite particle systems. We apply this strategy to energy minimizers of configurational energies featuring two-body short-ranged particle interactions and three-body angular potentials favoring bond-angles of the square lattice. To each configuration, we associate its bond graph which is then suitably modified by identifying chains of successive atoms. This method, called stratification, reduces the crystallization problem to a simple minimization that corresponds to a proof via slicing of the isoperimetric inequality in ℓ1 . As a byproduct, we also prove a fluctuation estimate for minimizers of the configurational energy, known as the n3 / 4 -law.

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Friedrich, M., & Kreutz, L. (2023). A Proof of Finite Crystallization via Stratification. Journal of Statistical Physics, 190(12). https://dx.doi.org/10.1007/s10955-023-03202-7


Friedrich, Manuel, and Leonard Kreutz. "A Proof of Finite Crystallization via Stratification." Journal of Statistical Physics 190.12 (2023).

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