Hard-disk equation of state: first-order liquid-hexatic transition in two dimensions with three simulation methods.
Michael Engel,Joshua A. Anderson,Sharon C. Glotzer,Masaharu Isobe,Masaharu Isobe,Etienne P. Bernard,Werner Krauth +6 more
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In this paper, large-scale computer simulations of the hard disk system at high densities in the region of the melting transition are presented, where the authors reproduce the equation of state, previously obtained using the event-chain Monte Carlo algorithm, with a massively parallel implementation of the local Monte Carlo method and with event-driven molecular dynamics.Abstract:
We report large-scale computer simulations of the hard-disk system at high densities in the region of the melting transition. Our simulations reproduce the equation of state, previously obtained using the event-chain Monte Carlo algorithm, with a massively parallel implementation of the local Monte Carlo method and with event-driven molecular dynamics. We analyze the relative performance of these simulation methods to sample configuration space and approach equilibrium. Our results confirm the first-order nature of the melting phase transition in hard disks. Phase coexistence is visualized for individual configurations via the orientational order parameter field. The analysis of positional order confirms the existence of the hexatic phase.read more
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The role of local structure in dynamical arrest
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Full Phase Diagram of Active Brownian Disks: From Melting to Motility-Induced Phase Separation.
Pasquale Digregorio,Demian Levis,Demian Levis,Antonio Suma,Antonio Suma,Leticia F. Cugliandolo,Giuseppe Gonnella,Ignacio Pagonabarraga,Ignacio Pagonabarraga +8 more
TL;DR: The complete phase diagram of self-propelled hard disks in two spatial dimensions is established from the analysis of the equation of state and the statistics of local order parameters.
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Elastic instability of a crystal growing on a curved surface.
TL;DR: The results illustrate the effects of curvature on the ubiquitous process of crystallization, with practical implications for nanoscale disorder-order transitions on curved manifolds, including the assembly of viral capsids, phase separation on vesicles, and crystallization of tetrahedra in three dimensions.
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Kosterlitz-Thouless physics: a review of key issues
TL;DR: The origins and the early work on transitions driven by topological defects such as vortices in the two dimensional planar rotor model and in (4)Helium films and dislocations and disclinations in 2D crystals are reviewed.
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Generalized event-chain Monte Carlo: constructing rejection-free global-balance algorithms from infinitesimal steps.
TL;DR: An event-driven algorithm is presented that generalizes the recent hard-sphere event-chain Monte Carlo method without introducing discretizations in time or in space and breaks detailed balance, but satisfies maximal global balance.
References
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Book
Statistical Mechanics: Algorithms and Computations
TL;DR: In this paper, Monte Carlo Methods are used for hard disks and spheres, density matrices and path integral, order and disorder in spin systems, and dynamic Monte-Carlo Methods.
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