Fetching the paper…
Reading the bibliography…
It is well-known that any Lennard-Jones type potential energy must have a periodic ground state given by a triangular lattice in dimension 2.
Universal optimality of the
H. Cohn, A. Kumar, S. D. Miller, D. Radchenko, and M. Viazovska · 1902
Earlier work this paper cites.
Zur Theorie allgemeiner Zetafunctionen
P. Epstein · 1903
Earlier work this paper cites.
Zur kinetischen Theorie der einatomigen Körper
G. Mie · 1903
Earlier work this paper cites.
On the determination of molecular fields II. From the equation of state of a gas
J. E. Jones · 1924
Earlier work this paper cites.
A Minimum Problem for the Epstein Zeta-Function
R. A. Rankin · 1953
Earlier work this paper cites.
On a Problem of Rankin about the Epstein Zeta-Function
J.W.S. Cassels · 1959
Earlier work this paper cites.
Notes on Two Lemmas concerning the Epstein Zeta-Function
P. H. Diananda · 1964
Earlier work this paper cites.
A Lemma about the Epstein Zeta-Function
V. Ennola · 1964
Earlier work this paper cites.
The Ground State for Sticky Disks
R. C. Heitmann and C. Radin · 1980
Earlier work this paper cites.
The Ground State for Soft Disks
C. Radin · 1981
Earlier work this paper cites.
Semiempirical, Quantum Mechanical Calculation of Hydrogen Embrittlement in Metals
M. S. Daw and M. I. Baskes · 1983
Earlier work this paper cites.
Low temperature and the origin of crystalline symmetry
C. Radin · 1987
Earlier work this paper cites.
Minimal Theta Functions
H. L. Montgomery · 1988
Earlier work this paper cites.
Harmonic Analysis on Symmetric Spaces and Applications II
A. Terras · 1988
Earlier work this paper cites.
The Riemann Zeta-Function
A. A. Karatsuba and S. M. Voronin · 1992
Earlier work this paper cites.
The embedded-atom method: a review of theory and applications
M. S. Daw, S. M. Foiles, and M. I. Baskes · 1993
Cited alongside, same era.
The Theory of Cubature Formulas
S. L. Sobolev and V. Vaskevitch · 1997
Cited alongside, same era.
Fast evaluation of the Epstein zeta functions
R. E. Crandall · 1998
Cited alongside, same era.
Understanding Molecular Simulation: from Algorithms to Applications
D. Frenkel and B. Smit · 2002
Cited alongside, same era.
A Numerical Investigation of the 2-Dimensional Crystal Problem
X. Blanc, C. Le Bris, and B. H. Yedder · 2003
Cited alongside, same era.
Intermolecular Interactions : Physical Picture, Computational Methods, Model Potentials
I. G. Kaplan · 2006
Cited alongside, same era.
The Hexagonal Lattice and the Epstein Zeta Function
A. Henn · 2016
Later among the works it cites.
Polytypism in the ground state structure of the Lennard-Jonesium
Lívia B. Pártay, Christoph Ortner, Albert P. Bartók, Chris J. Pickard, and Gábor Csányi · 2017
Later among the works it cites.
Harmonic Principles of Elemental Crystals — From Atomic Interaction to Fundamental Symmetry
M. Zschornak ans T. Leisegang, F. Meutzner, H. Stöcker, T. Lemser, T. Tauscher, C. Funke, C. Cherkouk, and D. C. Meyer · 2018
Later among the works it cites.
Local variational study of 2d lattice energies and application to Lennard-Jones type interactions
L. Bétermin · 2018
Later among the works it cites.
On Born’s conjecture about optimal distribution of charges for an infinite ionic crystal
L. Bétermin and H. Knüpfer · 2018
Later among the works it cites.
Crystallization in two dimensions and a discrete Gauss-Bonnet theorem
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Minima of Epstein’s Zeta Function and Heights of Flat Tori
P. Sarnak and A. Strömbergsson · 2006
Cited alongside, same era.
A Proof of Crystallization in Two Dimensions
F. Theil · 2006
Cited alongside, same era.
Energy Minimization, Periodic Sets and Spherical Designs
R. Coulangeon and A. Schürmann · 2012
Cited alongside, same era.
Minimizing atomic configurations of short range pair potentials in two dimensions: crystallization in the Wulff shape
G. Friesecke, B. Schmidt, and Y. A. Yeung · 2012
Cited alongside, same era.
Introduction to Computational Materials Science. Fundamentals to Applications
R. LeSar · 2013
Cited alongside, same era.
Minimization of energy per particle among Bravais lattices in
L. Bétermin and P. Zhang · 2015
Cited alongside, same era.
L. De Luca and G. Friesecke · 2018
Later among the works it cites.
Local optimality of cubic lattices for interaction energies
L. Bétermin · 2019
Later among the works it cites.
Optimal and non-optimal lattices for non-completely monotone interaction potentials
L. Bétermin and M. Petrache · 2019
Later among the works it cites.
Two-dimensional Wigner crystals of classical Lennard-Jones particles
I. Travěnec and L. Šamaj · 2019
Later among the works it cites.
On energy ground states among crystal lattice structures with prescribed bonds
L. Bétermin · 2021
Closest in time.
Lattice ground states for Embedded-Atom Models in 2D and 3D
L. Bétermin, M. Friedrich, and U. Stefanelli · 2021
Closest in time.
Crystallization to the square lattice for a two-body potential
L. Bétermin, L. De Luca, and M. Petrache · 2021
Closest in time.
Local energy optimality of periodic sets
R. Coulangeon and A. Schürmann · 2021
Closest in time.
Three-dimensional lattice ground states for Riesz and Lennard-Jones type energies
L. Bétermin, L. Šamaj, and I. Travěnec · 2022
Closest in time.