The crystallization conjecture: a review
Mathieu Lewin
Université de Cergy-Pontoise, FranceXavier Blanc
Université Denis Diderot (Paris 7), France
Abstract
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 where 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.
Cite this article
Mathieu Lewin, Xavier Blanc, The crystallization conjecture: a review. EMS Surv. Math. Sci. 2 (2015), no. 2, pp. 255–306
DOI 10.4171/EMSS/13