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TMF, 2017, Volume 191, Number 3, Pages 424–440 (Mi tmf9272)  

This article is cited in 5 scientific papers (total in 5 papers)

Renormalization group study of the melting of a two-dimensional system of collapsing hard disks

V. N. Ryzhov, E. E. Tareeva, Yu. D. Fomin, E. N. Tsiok, E. S. Chumakov

Vereshchagin Institute for High Pressure Physics, RAS, Moscow, Russia

Abstract: We consider the melting of a two-dimensional system of collapsing hard disks (a system with a hard-disk potential to which a repulsive step is added) for different values of the repulsive-step width. We calculate the system phase diagram by the method of the density functional in crystallization theory using equations of the Berezinskii–Kosterlitz–Thouless–Halperin–Nelson–Young theory to determine the lines of stability with respect to the dissociation of dislocation pairs, which corresponds to the continuous transition from the solid to the hexatic phase. We show that the crystal phase can melt via a continuous transition at low densities (the transition to the hexatic phase) with a subsequent transition from the hexatic phase to the isotropic liquid and via a first-order transition. Using the solution of renormalization group equations with the presence of singular defects (dislocations) in the system taken into account, we consider the influence of the renormalization of the elastic moduli on the form of the phase diagram.

Keywords: melting of two-dimensional system, Berezinskii–Kosterlitz–Thouless–Halperin–Nelson–Young theory, elastic modulus, hexatic phase.

Funding Agency Grant Number
Russian Science Foundation 14-12-00820
This research is supported by a grant from the Russian Science Foundation (Project No. 14-12-00820).


DOI: https://doi.org/10.4213/tmf9272

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English version:
Theoretical and Mathematical Physics, 2017, 191:3, 842–855

Bibliographic databases:

Received: 06.09.2016

Citation: V. N. Ryzhov, E. E. Tareeva, Yu. D. Fomin, E. N. Tsiok, E. S. Chumakov, “Renormalization group study of the melting of a two-dimensional system of collapsing hard disks”, TMF, 191:3 (2017), 424–440; Theoret. and Math. Phys., 191:3 (2017), 842–855

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/tmf/v191/i3/p424

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Gaiduk E.A. Fomin Yu.D. Tsiok E.N. Ryzhov V.N., “The Influence of Random Pinning on the Melting Scenario of Two-Dimensional Soft-Disk Systems”, Mol. Phys.  crossref  mathscinet  isi  scopus
    2. V. N. Ryzhov, E. E. Tareyeva, Yu. D. Fomin, E. N. Tsiok, “Berezinskii – Kosterlitz – Thouless transition and two-dimensional melting”, Phys. Usp., 60:9 (2017), 857–885  mathnet  crossref  crossref  adsnasa  isi  elib
    3. E. N. Tsiok, Y. D. Fomin, V. N. Ryzhov, “Random pinning elucidates the nature of melting transition in two-dimensional core-softened potential system”, Physica A, 490 (2018), 819–827  crossref  mathscinet  isi  scopus
    4. V. N. Ryzhov, E. E. Tareeva, “Possible scenarios of a phase transition from isotropic liquid to a hexatic phase in the theory of melting in two-dimensional systems”, Theoret. and Math. Phys., 200:1 (2019), 1053–1062  mathnet  crossref  crossref  adsnasa  isi  elib
    5. V. N. Ryzhov, E. E. Tareyeva, Yu. D. Fomin, E. N. Tsiok, “Complex phase diagrams of systems with isotropic potentials: results of computer simulations”, Phys. Usp., 63:5 (2020), 417–439  mathnet  crossref  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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