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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
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English version:
Theoretical and Mathematical Physics, 2011, 167:2, 645–653
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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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http://mi.mathnet.ru/eng/tmf6640https://doi.org/10.4213/tmf6640 http://mi.mathnet.ru/eng/tmf/v167/i2/p284
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This publication is cited in the following articles:
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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
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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
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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
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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
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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
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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
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