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TMF, 2011, Volume 167, Number 2, Pages 284–294 (Mi tmf6640)  

This article is cited in 6 scientific papers (total in 6 papers)

Singularity of the “swallow-tail” type and the glass–glass transition in a system of collapsing hard spheres

V. N. Ryzhov, E. E. Tareeva, Yu. D. Fomin

Institute for High Pressure Physics, RAS, Troitsk, Moscow Oblast, Russia

Abstract: In the mode-coupling approximation, we consider the transition to the glass state in a system of collapsing hard spheres (a system with the hard-core potential to which a repulsive step is added) We propose an approximation for the structure factor of the system, which we use to construct the phase diagram of the transition to the glass state. We show that there exists a maximum on the liquid–glass curve corresponding to the reentrant transition to the glass state in the system. In the framework of the proposed model, we consider bifurcations of solutions of the equations describing the transition to the glass state and show that there exist bifurcations of the “swallow-tail” type corresponding to the glass–glass transition.

Keywords: mode-coupling theory, liquid–glass transition, glass–glass transition

DOI: https://doi.org/10.4213/tmf6640

Full text: PDF file (473 kB)
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English version:
Theoretical and Mathematical Physics, 2011, 167:2, 645–653

Bibliographic databases:

Received: 15.11.2010

Citation: V. N. Ryzhov, E. E. Tareeva, Yu. D. Fomin, “Singularity of the “swallow-tail” type and the glass–glass transition in a system of collapsing hard spheres”, TMF, 167:2 (2011), 284–294; Theoret. and Math. Phys., 167:2 (2011), 645–653

Citation in format AMSBIB
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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. Ryzhov V.N., Tareyeva E.E., “A Toy Mct Model For Multiple Glass Transitions: Double Swallow Tail Singularity”, Phys. Lett. A, 378:47 (2014), 3567–3571  crossref  mathscinet  zmath  adsnasa  isi  scopus
    2. Brazhkin V.V. Fomin Yu.D. Ryzhov V.N. Tareyeva E.E. Tsiok E.N., “True Widom Line For a Square-Well System”, Phys. Rev. E, 89:4 (2014), 042136  crossref  adsnasa  isi  scopus
    3. Chumakov E.S. Fomin Y.D. Shangina E.L. Tareyeva E.E. Tsiok E.N. Ryzhov V.N., “Phase Diagram of the System With the Repulsive Shoulder Potential in Two Dimensions: Density Functional Approach”, Physica A, 432 (2015), 279–286  crossref  mathscinet  adsnasa  isi  elib  scopus
    4. E. E. Tareeva, V. N. Ryzhov, “Supercritical fluid of particles with a Yukawa potential: A new approximation for the direct correlation function and the Widom line”, Theoret. and Math. Phys., 189:3 (2016), 1806–1817  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    5. 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”, Theoret. and Math. Phys., 191:3 (2017), 842–855  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    6. 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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