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Melting Scenarios of Two-Dimensional Systems: Possibilities of Computer Simulation

  • STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS
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Abstract

Modern theories of melting of two-dimensional systems are discussed that are mainly based on the concepts of the Berezinskii–Kosterlitz–Thouless (BKT) theory of phase transitions in two-dimensional systems with continuous symmetry. Today there exist three basic scenarios of melting of two-dimensional crystals. First of all, this is the Berezinskii–Kosterlitz–Thouless–Halperin–Nelson–Young (BKTHNY) theory, in which two-dimensional crystals are melted through two BKT-type continuous transitions with an intermediate hexatic phase. In this case a first-order phase transition can also occur. The third scenario has recently been proposed by Bernard and Krauth (BK), in which melting can occur through a BKT-type transition; in this case the hexatic phase–isotropic fluid transition is a first-order transition. The review presents a critical analysis of the approaches used to determine the parameters and the type of transition by computer simulation methods.

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ACKNOWLEDGMENTS

The authors are grateful to V. V. Brazhkin and A. K. Murtazaev for their interest in the work and useful discussions of various aspects of the subject.

Funding

The work was supported by the Russian Science Foundation (grant no. 19-12-00092, https://rscf.ru/project/19-12-00092) and was carried out using the equipment of the Federal Collective Usage Center “Complex for Simulation and Data Processing for Mega-science Facilities” at the National Research Center ”Kurchatov Institute,” http://ckp.nrcki.ru, and the computing resources of the Joint Supercomputer Center of the Russian Academy of Sciences (JSCC RAS).

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  1. Vereshchagin Institute of High Pressure Physics, Russian Academy of Sciences, 108840, Troitsk, Moscow, Russia

    V. N. Ryzhov, E. A. Gaiduk, E. E. Tareeva, Yu. D. Fomin & E. N. Tsiok

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  1. V. N. Ryzhov
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Translated by I. Nikitin

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Ryzhov, V.N., Gaiduk, E.A., Tareeva, E.E. et al. Melting Scenarios of Two-Dimensional Systems: Possibilities of Computer Simulation. J. Exp. Theor. Phys. 137, 125–150 (2023). https://doi.org/10.1134/S1063776123070129

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