Related papers: Minimizing lattice structures for Morse potential …
The objective of this study is to evaluate the mechanical properties and energy absorption characteristics of the gyroid, dual-lattice and spinodoid structures, as biomimetic lattices, through finite element analysis and experimental…
We consider a lattice gas in spaces of dimensionality $\mathcal{D}=1,2,3$. The particles are subject to a hardcore exclusion interaction and an attractive pair interaction that satisfies Gauss' law as do Newtonian gravity in…
We demonstrate that inverse statistical mechanical optimization can be used to discover simple (e.g., short-range, isotropic, and convex-repulsive) pairwise interparticle potentials with three-dimensional diamond or simple cubic lattice…
We consider two-dimensional systems of point particles located on rectangular lattices and interacting via pairwise potentials. The goal of this paper is to investigate the phase transitions (and their nature) at fixed density for the…
We present two-dimensional crystallization results in the square lattice for finite particle systems consisting of two different atomic types. We identify energy minimizers of configurational energies featuring two-body short-ranged…
We prove strong crystallization results in two dimensions for an energy that arises in the theory of block copolymers. The energy is defined on sets of points and their weights, or equivalently on the set of atomic measures. It consists of…
Recent advances in spin-dependent optical lattices [Meng et al., Nature \textbf{615}, 231 (2023)] have enabled the experimental implementation of two superimposed three-dimensional lattices, presenting new opportunities to investigate…
We summarise status and recent results of the European Twisted Mass collaboration (ETMC). The collaboration has generated gauge configurations for three different values of the lattice spacing smaller or equal 0.1 fm and values of the…
A theoretical approach was developed for an exact numerical description of a pair of ultracold atoms interacting via a central potential that are trapped in a three-dimensional optical lattice. The coupling of center-of-mass and…
We analyze the impact of the lattice geometry on the thermodynamic transition to magnetically ordered phases in strongly interacting electron systems for various Bravais lattices in three and four dimensions, including both local and…
The static three-quark (3Q) potential is studied in detail using SU(3) lattice QCD with $12^3 \times 24$ at $\beta=5.7$ and $16^3 \times 32$ at $\beta=5.8$, 6.0 at the quenched level. For more than 300 different patterns of the 3Q systems,…
Using fully minimized fundamental measure functionals, we investigate free energies, vacancy concentrations and density distributions for bcc, fcc and hcp hard-sphere crystals. Results are complemented by an approach due to Stillinger which…
We investigate ground state configurations of atomic systems in two dimensions interacting via short range pair potentials. As the number of particles tends to infinity, we show that low-energy configurations converge to a macroscopic…
This work provides a rigorous analysis of Bain-type cuboidal lattice transformations, which connect the face-centered cubic (fcc), mean-centered cubic (mcc), body-centered cubic (bcc) and axially centered cubic (acc) lattices. Our study…
We formulate statistical-mechanical inverse methods in order to determine optimized interparticle interactions that spontaneously produce target many-particle configurations. Motivated by advances that give experimentalists greater and…
The low-energy theory of electrons interacting via repulsive short-range interactions on graphene's honeycomb lattice at half filling is presented. The exact symmetry of the Lagrangian with local quartic terms for the Dirac field dictated…
We study a harmonic triangular lattice, which relaxes in the presence of a weak, short-wavelength periodic potential. Monte Carlo simulations reveal that the elastic lattice has only short-ranged positional correlations, despite the absence…
Here, we investigate the fractal-lattice Hubbard model using various numerical methods: exact diagonalization, the self-consistent diagonalization of a (mean-field) Hartree-Fock Hamiltonian and state-of-the-art Auxiliary-Field Quantum Monte…
While the hexagonal lattice is ubiquitous in two dimensions, the body centered cubic lattice and the face centered lattice are both commonly observed in three dimensions. A geometric variational problem motivated by the diblock copolymer…
We use inverse methods of statistical mechanics and computer simulations to investigate whether an isotropic interaction designed to stabilize a given two-dimensional (2D) lattice will also favor an analogous three-dimensional (3D)…