4 research outputs found
Minimization of energy per particle among Bravais lattices in R^2 : Lennard-Jones and Thomas-Fermi cases
We study the two dimensional Lennard-Jones energy per particle of lattices
and we prove that the minimizer among Bravais lattices with sufficiently large
density is triangular and that is not the case for sufficiently small density.
We give other results about the global minimizer of this energy. Moreover we
study the energy per particle stemming from Thomas-Fermi model in two
dimensions and we prove that the minimizer among Bravais lattices with fixed
density is triangular. We use a result of Montgomery from Number Theory about
the minimization of Theta functions in the plane.Comment: 15 pages, 4 figures. Final Versio
Continuum percolation for Gibbsian point processes with attractive interactions
We study the problem of continuum percolation in infinite volume Gibbs measures for particles with an attractive pair potential, with a focus on low temperatures (large β). The main results are bounds on percolation thresholds ρ ± (β) in terms of the density rather than the chemical potential or activity. In addition, we prove a variational formula for a large deviations rate function for cluster size distributions. This formula establishes a link with the Gibbs variational principle and a form of equivalence of ensembles, and allows us to combine knowledge on finite volume, canonical Gibbs measures with infinite volume, grand-canonical Gibbs measure
Continuum percolation for Gibbsian point processes with attractive interactions
We study the problem of continuum percolation in infinite volume Gibbs
measures for particles with an attractive pair potential, with a focus on low
temperatures (large ). The main results are bounds on percolation
thresholds in terms of the density rather than the chemical
potential or activity. In addition, we prove a variational formula for a large
deviations rate function for cluster size distributions. This formula
establishes a link with the Gibbs variational principle and a form of
equivalence of ensembles, and allows us to combine knowledge on finite volume,
canonical Gibbs measures with infinite volume, grand-canonical Gibbs measures.Comment: 22 pages. Corrected a statement on lattice gases, added referenc