Crystallization in the Winterbottom Shape and Sharp Fluctuation Laws
Friedrich M, Kreutz L, Stefanelli U (2026)
Publication Type: Journal article
Publication year: 2026
Journal
Book Volume: 407
Article Number: 241
Journal Issue: 11
DOI: 10.1007/s00220-026-05729-8
Abstract
We address finite crystallization in two dimensions in the presence of a flat crystalline substrate. Particles interact through short-range two- and three-body potentials favoring local square-lattice arrangements. An additional interaction term of relative strength β>0 couples the particles and the substrate. Our first main result proves crystallization for all β>0, corresponding to the onset of discrete Winterbottom configurations. The proof relies on a stratification technique from [31], characterizing the topology of the bond graph of minimizing configurations. Our second main result concerns fluctuations estimates for β∈(0,1). We obtain bounds on the distance between distinct minimizers with the same number N of particles, showing a sharp scaling law N3/4 when β is rational, and N1/3 when β is irrational and algebraic. This reveals a genuine substrate-driven effect on fluctuation laws. As a corollary, we derive a discrete-to-continuum convergence of minimizers towards the Winterbottom equilibrium shape in the large-particle limit.
Authors with CRIS profile
Involved external institutions
Technische Universität München (TUM)
Germany (DE)
Universität Wien / University of Vienna
Austria (AT)
Germany (DE)
Universität Wien / University of Vienna
Austria (AT)
How to cite
APA:
Friedrich, M., Kreutz, L., & Stefanelli, U. (2026). Crystallization in the Winterbottom Shape and Sharp Fluctuation Laws. Communications in Mathematical Physics, 407(11). https://doi.org/10.1007/s00220-026-05729-8
MLA:
Friedrich, Manuel, Leonard Kreutz, and Ulisse Stefanelli. "Crystallization in the Winterbottom Shape and Sharp Fluctuation Laws." Communications in Mathematical Physics 407.11 (2026).
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