Crystallization to the Square Lattice for a Two-Body Potential

Simple item page
dc.contributor.authorBetermin, Laurent
dc.contributor.authorDe Luca, Lucia
dc.contributor.authorPetrache, Mircea
dc.date.accessioned2025-01-20T23:53:21Z
dc.date.available2025-01-20T23:53:21Z
dc.date.issued2021
dc.description.abstractWe consider two-dimensional zero-temperature systems of N particles towhich we associate an energy of the form
dc.description.abstractE[V](X) := Sigma(1 <= i<) j(<= N) V(|X(i) - X(j)|),
dc.description.abstractwhere X(j) is an element of R-2 represents the position of the particle j and V(r) is an element of R is the pairwise interaction energy potential of two particles placed at distance r. We show that under suitable assumptions on the single-well potential V, the ground state energy per particle converges to an explicit constant <(E)over bar>(sq[V]), which is the same as the energy per particle in the square lattice infinite configuration. We thus have
dc.description.abstractN (E) over bar (sq[V]) <= (X:{1,...,N}-> R2) E[V](X) <= N (E) over bar (sq)[V] + O(N-1/2). Moreover (E) over bar (sq)[V] is also re-expressed as the minimizer of a four point energy. In particular, this happens if the potential V is such that V(r) = +infinity for r < 1, V(r) = -1 for r is an element of [1, root 2], V(r) = 0 if r > root 2, in which case (E) over bar (sq)[V] = -4. To the best of our knowledge, this is the first proof of crystallization to the square lattice for a two-body interaction energy.
dc.fuente.origenWOS
dc.identifier.doi10.1007/s00205-021-01627-6
dc.identifier.eissn1432-0673
dc.identifier.issn0003-9527
dc.identifier.urihttps://doi.org/10.1007/s00205-021-01627-6
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/94957
dc.identifier.wosidWOS:000627657200002
dc.issue.numero2
dc.language.isoen
dc.pagina.final1053
dc.pagina.inicio987
dc.revistaArchive for rational mechanics and analysis
dc.rightsacceso restringido
dc.titleCrystallization to the Square Lattice for a Two-Body Potential
dc.typeartículo
dc.volumen240
sipa.indexWOS
sipa.trazabilidadWOS;2025-01-12
Files
Collections
Artículos de revistas