Dynamical arrest with zero complexity: The unusual behavior of the spherical Blume-Emery-Griffiths disordered model
- 31 December 2015
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 92 (6), 062150
- https://doi.org/10.1103/physreve.92.062150
Abstract
The short- and long-time dynamics of model systems undergoing a glass transition with apparent inversion of Kauzmann and dynamical arrest glass transition lines is investigated. These models belong to the class of the spherical mean-field approximation of a spin-1 model with -body quenched disordered interaction, with , termed spherical Blume-Emery-Griffiths models. Depending on temperature and chemical potential the system is found in a paramagnetic or in a glassy phase and the transition between these phases can be of a different nature. In specific regions of the phase diagram coexistence of low-density and high-density paramagnets can occur, as well as the coexistence of spin-glass and paramagnetic phases. The exact static solution for the glassy phase is known to be obtained by the one-step replica symmetry breaking ansatz. Different scenarios arise for both the dynamic and the thermodynamic transitions. These include: (i) the usual random first-order transition (Kauzmann-like) for mean-field glasses preceded by a dynamic transition, (ii) a thermodynamic first-order transition with phase coexistence and latent heat, and (iii) a regime of apparent inversion of static transition line and dynamic transition lines, the latter defined as a nonzero complexity line. The latter inversion, though, turns out to be preceded by a dynamical arrest line at higher temperature. Crossover between different regimes is analyzed by solving mode-coupling-theory equations near the boundaries of paramagnetic solutions and the relationship with the underlying statics is discussed.
Keywords
Funding Information
- Russian Foundation for Basic Research (RBFR08M3P4)
- Seventh Framework Programme (FP7/2007-2013/)
- Research Executive Agency (290038)
- European Research Council (247328)
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