Existence of a hexatic phase between 2D solid and liquid
In plain words
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 statement
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.
What would settle it
A proof of the two distinct decay laws in a nonempty parameter region of a 2D continuum model.