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Possible Scenarios of a Phase Transition from Isotropic Liquid to a Hexatic Phase in the Theory of Melting in Two-Dimensional Systems

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Abstract

A two-stage process consisting of two continuous Berezinskii-Kosterlitz-Thouless-type transitions with an intermediate anisotropic liquid, a hexatic phase, is a well-known scenario of melting in two-dimensional systems. A direct first-order transition, similar to melting in three-dimensional systems, is another scenario variant. We prove the possibility in principle of the existence of a third scenario according to which melting occurs via two transitions, but in contrast to predictions of the Berezinskii-Kosterlitz-Thouless theory, the transition from an isotropic liquid to a hexatic phase is a first-order transition. Such a scenario was recently observed in a computer simulation of two-dimensional systems and then in a real experiment. Our proof is based on an analysis of branching solutions of an exact closed nonlinear integral equation for a two-particle conditional distribution function.

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Authors and Affiliations

  1. Vereshchagin Institute for High Pressure Physics, RAS, Troitsk, Moscow Oblast, Russia

    V. N. Ryzhov & E. E. Tareyeva

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  1. V. N. Ryzhov
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  2. E. E. Tareyeva
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Correspondence to E. E. Tareyeva.

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This research was supported by the Russian Foundation for Basic Research (Grant No. 17-02-00320).

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 200, No. 1, pp. 147–157, July, 2019.

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Ryzhov, V.N., Tareyeva, E.E. Possible Scenarios of a Phase Transition from Isotropic Liquid to a Hexatic Phase in the Theory of Melting in Two-Dimensional Systems. Theor Math Phys 200, 1053–1062 (2019). https://doi.org/10.1134/S0040577919070092

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