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Abstract
The behavior of a family of mean-field glass models is reviewed. The models are analysed by means of a Langevin-based approach to the dynamics and a replica theory computation of the thermodynamics. We focus on the phase diagram of a particular model case, where glass-to-glass transitions occur between phases with a different number of characteristic time-scales for the relaxation processes. The appearance of Johari-Goldstein processes as collective reorganizations of sets of fast processes is discussed.
Notes
1. Glassy models without quenched disorder can be devised as well; see, e.g. Citation5–7.
2. Many examples of polyamorphism are available in nature (and in the literature). For example, the change in the kinetics of the coordination between molecules, occurring in vitreous germania and silica Citation8–10 or the sharp density change taking place in porous silicon Citation11, as well as in undercooled water Citation12. Very recently polyamorphism in ethanol Citation13, laponite Citation14,Citation15 and star polymer mixtures has been observed.
3. A well-known example is the symbolic dynamics through the potential energy landscape, where intra-basin processes have a high correlation and inter-basin processes have a low correlation Citation17,Citation18.
4. From the point of view of replica calculation we stress that a thermodynamically consistent example of a 2RSB phase has not been realized in models other than the s + p spherical models Citation22.
5. Usually, a glass phase is associated with discontinuous steps in the overlap, corresponding to a sharp separation of time-scales. A spin-glass phase is, instead, characterized by a fully continuous q(x).
6. We notice that the experimental, calorimetric, glass temperature T g is not defined in mean-field systems. Indeed, this is a property connected with the falling out of equilibrium of activated processes (hopping among valleys), whereas in mean-field metastable states are surrounded by infinite barriers (as N → ∞). T g lies, undetermined, between T K and T d .
7. For details of the generalization of equilibrium dynamics in the solid amorphous phase see Citation25).
8. The thermodynamic transition, termed ‘Kauzmann’ in the figure, is a so-called ‘random first-order transition’, with no latent heat but a discontinuous order parameter. This is an example of the mean-field scenario behind the mosaic theory Citation4.
9. At higher temperature the global minimum is a liquid/paramagnetic state.