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Title: Finite-temperature phase diagram of a two-dimensional supersolid
Plain: In two dimensions, heat destroys perfect crystal and superfluid order, leaving only slowly decaying versions. How these two partial orders melt, together or one after another, is unknown.
Precise: Infinite 2D dipolar Bose gas in its supersolid regime at $T > 0$. Crystal and phase order are at most quasi-long-range. Classify the sequence of transitions (Berezinskii-Kosterlitz-Thouless superfluid loss, dislocation-mediated melting, possible hexatic or modulated-superfluid intermediate phases) with their critical behavior. Answer: phase diagram in ($T, a_s/a_{dd}$, density).
Settled by: Finite-temperature simulations (for example path-integral Monte Carlo) of the 2D dipolar gas with scaling analysis, confirmed by measured correlation functions.
Kind: well-posed
Answer type: classification
References: (empty)
Literature status: open
Status note: 2D supersolid arrays have been made since 2021 (Norcia et al., Nature 2021) and a 2D stripe supersolid in Er was reported in 2025 (arXiv:2512.13280); no measurement or simulation has resolved the finite-T transition sequence.
Posed since: (empty)