Minimizing lattice structures for Morse potential energy in two and three dimensions
From MaRDI portal
Publication:5205174
DOI10.1063/1.5091568zbMath1431.82004arXiv1901.08957OpenAlexW3104212259MaRDI QIDQ5205174
Publication date: 10 December 2019
Published in: Journal of Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1901.08957
Statistical mechanics of crystals (82D25) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)
Related Items
Supersonic voidions in 2D Morse lattice ⋮ On minima of difference of theta functions and application to hexagonal crystallization ⋮ ON A LATTICE GENERALISATION OF THE LOGARITHM AND A DEFORMATION OF THE DEDEKIND ETA FUNCTION ⋮ Lattice ground states for embedded-atom models in 2D and 3D ⋮ Effect of periodic arrays of defects on lattice energy minimizers ⋮ On the optimality of the rock-salt structure among lattices with charge distributions ⋮ Crystallization to the square lattice for a two-body potential ⋮ Optimal and non-optimal lattices for non-completely monotone interaction potentials ⋮ Theta Functions and Optimal Lattices for a Grid Cells Model ⋮ On minima of sum of theta functions and application to Mueller-Ho conjecture ⋮ An extremal property of the hexagonal lattice ⋮ Minimal soft lattice theta functions ⋮ On energy ground states among crystal lattice structures with prescribed bonds
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- From the Ginzburg-Landau model to vortex lattice problems
- Face-centered cubic crystallization of atomistic configurations
- Application of an idea of Voronoĭ to lattice zeta functions
- Minimal soft lattice theta functions
- On the crystallization of 2D hexagonal lattices
- A proof of crystallization in two dimensions
- Lowest Landau level functional and Bargmann spaces for Bose-Einstein condensates
- The crystallization conjecture: a review
- An application of the modular function in nonlocal variational problem
- On Born's conjecture about optimal distribution of charges for an infinite ionic crystal
- Crystallization in two dimensions and a discrete Gauss-Bonnet theorem
- Optimal lattice configurations for interacting spatially extended particles
- Chaotic eigenfunctions in phase space.
- Local optimality of cubic lattices for interaction energies
- Crystallization in carbon nanostructures
- Existence of compactly supported global minimisers for the interaction energy
- Minima of Epstein's zeta function and heights of flat tori
- Two-Dimensional Theta Functions and Crystallization among Bravais Lattices
- Nonlocal Aggregation Models: A Primer of Swarm Equilibria
- New Duality Relations for Classical Ground States
- Energy Minimization, Periodic Sets and Spherical Designs
- On a problem of Rankin about the Epstein zeta-function
- Universally optimal distribution of points on spheres
- Spherical designs and zeta functions of lattices
- Minimization of energy per particle among Bravais lattices in ℝ2: Lennard–Jones and Thomas–Fermi cases
- Minimal theta functions
- Local variational study of 2d lattice energies and application to Lennard–Jones type interactions
- Approximate Global Minimizers to Pairwise Interaction Problems via Convex Relaxation
- Crystallization in the hexagonal lattice for ionic dimers
- A lemma about the Epstein zeta-function
- Notes on two lemmas concerning the Epstein zeta-function
- Dimension reduction techniques for the minimization of theta functions on lattices
- Finite crystallization in the square lattice
- A Minimum Problem for the Epstein Zeta-Function
