Crystallization for Coulomb and Riesz interactions as a consequence of the Cohn-Kumar conjecture

DOI10.1090/proc/15003zbMath1439.52025arXiv1908.09714OpenAlexW3012142882WikidataQ123138066 ScholiaQ123138066MaRDI QIDQ5111515

Sylvia Serfaty, Mircea Petrache

Publication date: 27 May 2020

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1908.09714

zbMATH Keywords

triangular latticeCoulomb interactioncrystallizationjelliumAbrikosov latticerenormalized energyWigner crystalCohn-Kumar conjectureRiesz interaction

Mathematics Subject Classification ID

Interacting particle systems in time-dependent statistical mechanics (82C22) Arrangements of points, flats, hyperplanes (aspects of discrete geometry) (52C35) Lattices and convex bodies (number-theoretic aspects) (11H06) Discrete geometry (52C99) Lattice packing and covering (number-theoretic aspects) (11H31) Classical dynamic and nonequilibrium statistical mechanics (general) (82C05)

Related Items (17)

Coulomb and Riesz gases: The known and the unknown ⋮ Number-rigidity and \(\beta\)-circular Riesz gas ⋮ Minimal Riesz energy on balanced fractal sets ⋮ New directions in real algebraic geometry. Abstracts from the workshop held March 19--24, 2023 ⋮ The Diamond ensemble: a constructive set of spherical points with small logarithmic energy ⋮ On the logarithmic energy of points on \(\mathbb{S}^2\) ⋮ Three‐dimensional lattice ground states for Riesz and Lennard‐Jones–type energies ⋮ Gaussian fluctuations and free energy expansion for Coulomb gases at any temperature ⋮ Lattices with finite renormalized Coulombian interaction energy in the plane ⋮ Effect of periodic arrays of defects on lattice energy minimizers ⋮ Asymptotic optimality of the triangular lattice for a class of optimal location problems ⋮ Crystallization to the square lattice for a two-body potential ⋮ Floating Wigner crystal and periodic jellium configurations ⋮ Nonhexagonal Lattices From a Two Species Interacting System ⋮ Discrepancy of minimal Riesz energy points ⋮ On energy ground states among crystal lattice structures with prescribed bonds ⋮ The boundary density profile of a Coulomb droplet. Freezing at the edge

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