The crystallization conjecture: a review (Q902281)

The paper is devoted to a review of the crystallization conjecture, studied since 1960, without being solved. Consider a physical system with \(N\) particles. For this system the (crystallization) question is: Does the system become periodic in the limit \(N\to\infty\)? Mathematically, it is related to study the minima of a real-valued function defined on \(\mathbb R^{3N}\). In the paper, the existing literature is reviewed. Several related open problems are mentioned.