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

Abstract

In this paper I will approach the computation of the maximum density of regular lattices in large dimensions using a statistical mechanics approach. The starting point will be some theorems of Roger, which are virtually unknown in the community of physicists. Using his approach one can see that there are many similarities (and differences) with the problem of computing the entropy of a liquid of perfect spheres. The relation between the two problems is investigated in details. Some conjectures are presented, that need further investigation in order to check their consistency.

27 pages

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Cited by in corpus (10)

• Mean field theory of hard sphere glasses and jamming
• Optimal Packings of Superballs
• Random perfect lattices and the sphere packing problem
• Jammed lattice sphere packings
• Studies of the Lennard-Jones fluid in 2, 3, and 4 dimensions highlight the need for a liquid-state 1/d expansion
• Statistical mechanics of the lattice sphere packing problem
• Generating dense packings of hard spheres by soft interaction design
• Application of Edwards' statistical mechanics to high dimensional jammed sphere packings
• Dynamic Space Packing
• Volumes for ${\mathrm{SL}}_N(\mathbb{R})$, the Selberg integral and random lattices