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Advanced Statistical Mechanics$
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Barry M McCoy

Print publication date: 2009

Print ISBN-13: 9780199556632

Published to Oxford Scholarship Online: February 2010

DOI: 10.1093/acprof:oso/9780199556632.001.0001

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Theorems on order

Theorems on order

(p.92) 4 Theorems on order
Advanced Statistical Mechanics

Barry M. McCoy

Oxford University Press

This chapter discusses Hales proof of Kepler's conjecture for densest packing of hard spheres and recent extensions to hard ellipsoids. It gives the proofs of lack of certain types of order in one and two dimensions. It discusses the proofs of existence of ferromagnetic and antiferromagnetic order in classical and quantum Heisenberg magnets in three dimensions. Open questions and ‘missing theorems’ are presented.

Keywords:   densest packing, Kepler, Heisenberg magnets, Hale

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