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Title: Crystalline phase of hard spheres at high packing fraction
Plain: Hard balls with no attraction freeze into a crystal when packed densely enough, as computer simulations show above about 55 percent filling. Prove that such a crystalline equilibrium state exists.
Precise: For hard spheres of diameter $a$ in $R^3$ at packing fraction $\eta$ close to the close-packing value $\pi/\sqrt{18}$, about 0.7405, prove existence of a non-translation-invariant Gibbs measure, and more sharply a first-order freezing transition; simulations place fluid-solid coexistence at $\eta$ about 0.494 and 0.545.
Settled by: A rigorous proof of crystalline long-range order for hard spheres at some $\eta$ below close packing.
Kind: well-posed
Answer type: yes-no
References: (empty)
Literature status: open
Status note: (empty)
Posed since: 1957