Extreme lattices: Symmetries and decorrelation

A. Andreanov, A. Scardicchio, S. Torquato

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

We study statistical and structural properties of extreme lattices, which are the local minima in the density landscape of lattice sphere packings in d-dimensional Euclidean space . Specifically, we ascertain statistics of the densities and kissing numbers as well as the numbers of distinct symmetries of the packings for dimensions 8 through 13 using the stochastic Voronoi algorithm. The extreme lattices in a fixed dimension of space d (d≥8) are dominated by typical lattices that have similar packing properties, such as packing densities and kissing numbers, while the best and the worst packers are in the long tails of the distribution of the extreme lattices. We also study the validity of the recently proposed decorrelation principle, which has important implications for sphere packings in general. The degree to which extreme-lattice packings decorrelate as well as how decorrelation is related to the packing density and symmetry of the lattices as the space dimension increases is also investigated. We find that the extreme lattices decorrelate with increasing dimension, while the least symmetric lattices decorrelate faster.

Original languageEnglish (US)
Article number113301
JournalJournal of Statistical Mechanics: Theory and Experiment
Volume2016
Issue number11
DOIs
StatePublished - Nov 10 2016

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Energy landscapes
  • Random/ordered microstructures
  • Spin glasses
  • Structural correlations

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