Two-step melting in two dimensions: First-order liquid-hexatic transition

Abstract

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 on after fifty 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.

5 pages, 4 figures

Cited by in corpus (269)

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• 2D Melting: From Liquid-Hexatic Coexistence to Continuous Transitions
• Models and algorithms for the next generation of glass transition studies
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• Crystallization in a dense suspension of self-propelled particles
• Assembly and Phase Transitions within Colloidal Crystals
• Equilibrium sampling of hard spheres up to the jamming density and beyond
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• Tunable long range forces mediated by self-propelled colloidal hard spheres
• Dual gauge field theory of quantum liquid crystals in two dimensions
• Generalized event-chain Monte Carlo: Constructing rejection-free global-balance algorithms from infinitesimal steps
• Thermodynamic phases in two-dimensional active matter
• Basic Understanding of Condensed Phases of Matter via Packing Models
• Long Wavelength Fluctuations and the Glass Transition in 2D and 3D
• Rejection-free Monte-Carlo sampling for general potentials
• The Role of Short-Range Order and Hyperuniformity in the Formation of Band Gaps in Disordered Photonic Materials
• Melting a skyrmion lattice topologically: through the hexatic phase to a skyrmion liquid
• Two-dimensional melting under quenched disorder
• Crystal nucleation as the ordering of multiple order parameters
• Two-stage melting induced by dislocations and grain boundaries in Monolayers of Hard Spheres
• Phase Diagram of Active Brownian Spheres: Crystallization and the Metastability of Motility-Induced Phase Separation
• Unveiling Dimensionality Dependence of Glassy Dynamics: 2D Infinite Fluctuation Eclipses Inherent Structural Relaxation
• Cooperative Strings and Glassy Interfaces
• Colloidal Hard Spheres: Triumphs, Challenges and Mysteries
• Crystallization of self-propelled hard-discs : a new scenario
• Purely hydrodynamic ordering of rotating disks at a finite Reynolds number
• Hard-body models of bulk liquid crystals
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• Dual gauge field theory of quantum liquid crystals in three dimensions
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• Phase co-existence in bidimensional passive and active dumbbell systems
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• Lindemann melting criterion in two dimensions
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• Assessing the role of static lengthscales behind glassy dynamics in polydisperse hard disks
• Point-to-set lengths, local structure, and glassiness
• Phase diagram of two-dimensional hard ellipses
• Unsupervised machine learning for detection of phase transitions in off-lattice systems I. Foundations
• Specific heat in two-dimensional melting
• Hard-sphere melting and crystallization with event-chain Monte Carlo
• Hexatic phase and water-like anomalies in a two-dimensional fluid of particles with a weakly softened core
• Event-chain Monte Carlo: foundations, applications, and prospects
• Disappearance of the hexatic phase in a binary mixture of hard disks
• Fluids in Extreme Confinement
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• The Liquid--Hexatic Transition for Soft Disks
• Anomalous Melting Scenario of the Two-Dimensional Core-Softened System
• PDMP characterisation of event-chain Monte Carlo algorithms for particle systems
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• Systematic Analysis of Crystalline Phases in Bosonic Lattice Models with Algebraically Decaying Density-Density Interactions
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• Topological Order in an Antiferomagnetic Tetratic
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• Pre-transition effects mediate forces of assembly between transmembrane proteins
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• Anisotropic skyrmion liquid phase
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• On the nature of the phase transitions in two-dimensional type II superconductors
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• Wulff shape for equilibrium phases
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