Nature of the melting transition in ideal noncrystals

Determine whether the melting of two-dimensional ideal noncrystals is described by a continuous Kosterlitz–Thouless-type phase transition (potentially of nonequilibrium character) or by the two-step Kosterlitz–Thouless–Halperin–Nelson–Young (KTHNY) scenario; characterize the associated phase behavior and critical properties governing this melting process.

Background

The paper introduces ideal noncrystals (INC) and develops a path-integral-like correlation function to reveal long-range structural correlations despite the absence of conventional symmetry breaking. Upon heating, the authors observe behavior reminiscent of two-dimensional melting and compare their correlation function with standard hexatic order correlations.

They note similarities to hexatic crystals and raise the question of the correct melting mechanism for INC—whether it follows a continuous KT-type transition or a two-step KTHNY scenario—highlighting the need for a detailed phase-transition characterization.