Melting mechanism of two-dimensional classical solids

Determine whether two-dimensional classical solids melt, as temperature increases, via a first-order phase transition or via a continuous transition through an intermediate hexatic phase, in order to resolve the long-standing uncertainty about the nature of melting in two dimensions.

Background

The paper studies the zero-temperature phase diagram of two-dimensional helium-4 and discusses melting scenarios, including possible intermediate hexatic phases. In classical two-dimensional systems, the Kosterlitz–Thouless–Halperin–Nelson–Young (KTHNY) theory predicts a two-step continuous melting involving a hexatic phase, while other evidence supports a first-order transition. Despite extensive classical simulations, the precise mechanism of melting in two-dimensional classical solids has remained unresolved for decades.

The authors reference this longstanding issue to motivate examining analogous scenarios in the quantum field at zero temperature. Their neural quantum state approach allows probing structural order and potential intermediate phases, but the classical problem itself remains explicitly stated as unresolved.