2011/02/28 by Etienne P. Bernard, Werner Krauth · 4 citations
Engineering · Materials Science · Mathematics · Physics and Astronomy · #Condensed matter physics #Liquid phase #Material Dynamics and Properties #Materials science #Mathematics #Monte Carlo method #Order (exchange) #Phase Equilibria and Thermodynamics #Phase transition #Physics #Statistical physics #Theoretical and Computational Physics #Theoretical physics #Thermalisation #Thermodynamics #cond-mat.soft #cond-mat.stat-mech #physics.comp-ph
paper · pdf · doi:10.1103/physrevlett.107.155704
published as Phys. Rev. Lett. 107, 155704 (2011) · 5 pages, 4 figures
arxiv created 2011/08/30 · openalex publication_date 2011/10/07 · arxiv updated 2015/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Melting in two spatial dimensions, as realized in thin films or at interfaces, represents one of the most fascinating phase transitions in nature, but it remains poorly understood. Even for the fundamental hard-disk model, the melting mechanism has not been agreed upon after 50 years of studies. A recent Monte Carlo algorithm allows us to thermalize systems large enough to access the thermodynamic regime. We show that melting in hard disks proceeds in two steps with a liquid phase, a hexatic phase, and a solid. The hexatic-solid transition is continuous while, surprisingly, the liquid-hexatic transition is of first order. This melting scenario solves one of the fundamental statistical-physics models, which is at the root of a large body of theoretical, computational, and experimental research.