On the most compact regular lattices in large dimensions: A statistical mechanical approach

DOI10.1007/s10955-008-9539-6zbMath1144.82014arXiv0710.0882OpenAlexW2114926067MaRDI QIDQ944968

Giorgio Parisi

Publication date: 10 September 2008

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0710.0882

zbMATH Keywords

lattice packingMinkowski theoremvirial expansionmost compact lattices

Mathematics Subject Classification ID

Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) (82D30) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Kinetic theory of gases in time-dependent statistical mechanics (82C40)

Related Items (2)

Volumes for \(\text{SL}_N(\mathbb{R})\), the Selberg integral and random lattices ⋮ Extreme lattices: symmetries and decorrelation

Cites Work

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• On the high density behavior of Hamming codes with fixed minimum distance
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• Mean values over the space of lattices
• Random-energy model: An exactly solvable model of disordered systems
• The Number of Lattice Points in a Set
• The Packing of Equal Spheres
• New Conjectural Lower Bounds on the Optimal Density of Sphere Packings

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