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

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

2007-10-03

arxiv.org/abs/0710.0882v1

Physics

Condensed Matter

Statistical Mechanics

27 pages

Scientific paper

10.1007/s10955-008-9539-6

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.

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