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Accepted · first revision · record

Title: Existence of a hexatic phase between 2D solid and liquid
Plain: Theory predicts that 2D crystals melt in two steps through an intermediate hexatic phase, in which bond directions stay aligned while positions are disordered as in a liquid. Prove such a phase exists for some particle system.
Precise: For hard disks or a 2D system with smooth repulsion, prove existence of a range of $(T, \rho)$ where positional correlations decay exponentially while bond-orientational correlations $\langle\psi_6(x)\,\psi_6(0)*\rangle$ decay as a power law, as in the Kosterlitz-Thouless-Halperin-Nelson-Young melting scenario. Hard-disk simulations (Bernard, Krauth 2011) find a hexatic phase near packing fraction 0.70 to 0.72 with a first-order liquid-hexatic transition.
Settled by: A proof of the two distinct decay laws in a nonempty parameter region of a 2D continuum model.
Kind: well-posed
Answer type: yes-no
References: (empty)
Literature status: open
Status note: (empty)
Posed since: 1978