Geodesic
The crystallization conjecture: a review
Xavier Blanc1 ; Mathieu Lewin2
1Université Denis Diderot (Paris 7), France
2Université de Cergy-Pontoise, France
EMS surveys in mathematical sciences, Tome 2 (2015) no. 2, pp. 255-306

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DOI

In this article we describe the crystallization conjecture. It states that, in appropriate physical conditions, interacting particles always place themselves into periodic configurations, breaking thereby the natural translation-invariance of the system. This famous problem is still largely open. Mathematically, it amounts to studying the minima of a real-valued function defined on R3N where N is the number of particles, which tends to infinity. We review the existing literature and mention several related open problems, of which many have not been thoroughly studied.
DOI : 10.4171/emss/13
Classification : 82-XX, 11-XX, 35-XX, 49-XX
Mots-clés : Crystallization conjecture, lattice, thermodynamic limit, Epstein zeta function, Wigner problem

Xavier Blanc  1   ; Mathieu Lewin  2

1 Université Denis Diderot (Paris 7), France
2 Université de Cergy-Pontoise, France 
Xavier Blanc; Mathieu Lewin. The crystallization conjecture: a review. EMS surveys in mathematical sciences, Tome 2 (2015) no. 2, pp. 255-306. doi: 10.4171/emss/13
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