Finite Crystallization and Wulff shape emergence for ionic compounds in the square lattice

DOI10.1088/1361-6544/ab591fzbMath1434.82084arXiv1903.00331OpenAlexW3100459015MaRDI QIDQ5215407

Leonard Kreutz, Manuel Friedrich

Publication date: 10 February 2020

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.00331

zbMATH Keywords

ground statesquare latticecrystallizationWulff shapenet chargeionic dimersconfigurational energy minimization

Mathematics Subject Classification ID

Interacting particle systems in time-dependent statistical mechanics (82C22) Statistical mechanics of crystals (82D25) Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics (82C20)

Related Items (14)

Note on crystallization for alternating particle chains ⋮ Crystallization in a one-dimensional periodic landscape ⋮ Maximal fluctuations on periodic lattices: an approach via quantitative Wulff inequalities ⋮ A compactness theorem for functions on Poisson point clouds ⋮ Crystallinity of the Homogenized Energy Density of Periodic Lattice Systems ⋮ The double-bubble problem on the square lattice ⋮ Emergence of Wulff-crystals from atomistic systems on the FCC and HCP lattices ⋮ A proof of finite crystallization via stratification ⋮ Effect of periodic arrays of defects on lattice energy minimizers ⋮ On the optimality of the rock-salt structure among lattices with charge distributions ⋮ Emergence of rigid polycrystals from atomistic systems with Heitmann-Radin sticky disk energy ⋮ Crystallization to the square lattice for a two-body potential ⋮ Crystallization in the hexagonal lattice for ionic dimers ⋮ On energy ground states among crystal lattice structures with prescribed bonds

Cites Work

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• Maximal fluctuations on periodic lattices: an approach via quantitative Wulff inequalities
• \(N^{3/4}\) law in the cubic lattice
• Minimizing atomic configurations of short range pair potentials in two dimensions: crystallization in the Wulff shape
• Ground states of the 2D sticky disc model: fine properties and \(N^{3/4}\) law for the deviation from the asymptotic Wulff shape
• Wulff shape emergence in graphene
• Crystallization in the hexagonal lattice for ionic dimers
• Finite crystallization in the square lattice
• Chain-like ground states in three dimensions

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