TY - JOUR
T1 - Extreme lattices
T2 - Symmetries and decorrelation
AU - Andreanov, A.
AU - Scardicchio, A.
AU - Torquato, S.
N1 - Funding Information:
ST was supported in part by the National Science Foundation under Grant No. DMS-1211087. This work was partially supported by a grant from the Simons Foundation (Grant No. 231015 to Salvatore Torquato). AA was supported by Project Code(IBS-R024-D1).
Publisher Copyright:
© 2016 IOP Publishing Ltd and SISSA Medialab srl.
PY - 2016/11/10
Y1 - 2016/11/10
N2 - 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.
AB - 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.
KW - Energy landscapes
KW - Random/ordered microstructures
KW - Spin glasses
KW - Structural correlations
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U2 - 10.1088/1742-5468/2016/11/113301
DO - 10.1088/1742-5468/2016/11/113301
M3 - Article
AN - SCOPUS:85001944908
VL - 2016
JO - Journal of Statistical Mechanics: Theory and Experiment
JF - Journal of Statistical Mechanics: Theory and Experiment
SN - 1742-5468
IS - 11
M1 - 113301
ER -