A note on weakly discontinuous dynamical transitions

Franz, Silvio; Parisi, G.; Ricci-Tersenghi, Federico; Rizzo, Tommaso; Urbani, Pierfrancesco

doi:10.1063/1.4790517

Cited by 8 publications

(1 citation statement)

References 35 publications

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“…A remarkable example is the HNC approximation, where one can find equations similar to Mode Coupling Theory, but in the context of a fully consistent theory. Work is on the way in this direction [27].…”

Section: Perspectivesmentioning

confidence: 99%

Quasi-equilibrium in glassy dynamics: an algebraic view

Franz

Parisi

2013

J. Stat. Mech.

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We study a chain of identical glassy systems in a constrained equilibrium where each bond of the chain is forced to remain at a preassigned distance to the previous one. We apply this description to Mean Field Glassy systems in the limit of long chain where each bond is close to the previous one. We show that in specific conditions this pseudo-dynamic process can formally describe real relaxational dynamics for long times. In particular, in mean field spin glass models we can recover in this way the equations of Langevin dynamics in the long time limit at the dynamical transition temperature and below. We interpret the formal identity as an evidence that in these situations the configuration space is explored in a quasi-equilibrium fashion. Our general formalism, that relates dynamics to equilibrium, puts slow dynamics in a new perspective and opens the way to the computation of new dynamical quantities in glassy systems.

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Section: Perspectivesmentioning

confidence: 99%

Quasi-equilibrium in glassy dynamics: an algebraic view

Franz

Parisi

2013

J. Stat. Mech.

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Universality classes of critical points in constrained glasses

Franz

Parisi

2013

J. Stat. Mech.

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We analyze critical points that can be induced in glassy systems by the presence of constraints.These critical points are predicted by the Mean Field Thermodynamic approach and they are precursors of the standard glass transition in absence of constraints. Through a deep analysis of the soft modes appearing in the replica field theory we can establish the universality class of these points. In the case of the "annealed potential" of a symmetric coupling between two copies of the system, the critical point is in the Ising universality class. More interestingly, is the case of the "quenched potential" where the a single copy is coupled with an equilibrium reference configuration, or the "pinned particle" case where a fraction of particles is frozen in fixed positions. In these cases we find the Random Field Ising Model (RFIM) universality class. The effective random field is a "self-generated" disorder that reflects the random choice of the reference configuration. The RFIM representation of the critical theory predicts non-trivial relations governing the leading singular behavior of relevant correlation functions, that can be tested in numerical simulations.

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Quasi equilibrium construction for the long time limit of glassy dynamics

et al. 2015

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In this paper we review a recent proposal to understand the long time limit of glassy dynamics in terms of an appropriate Markov Chain. [1]. The advantages of the resulting construction are many. The first one is that it gives a quasi equilibrium description on how glassy systems explore the phase space in the slow relaxation part of their dynamics. The second one is that it gives an alternative way to obtain dynamical equations starting from a dynamical rule that is static in spirit. This provides a way to overcome the difficulties encountered in the short time part of the dynamics where current conservation must be enforced. We study this approach in detail in a prototypical mean field disordered spin system, namely the p-spin spherical model, showing how we can obtain the well known equations that describes its dynamics. Then we apply the same approach to structural glasses. We first derive a set of dynamical Ornstein-Zernike equations which are very general in nature. Finally we consider two possible closure schemes for them, namely the Hypernetted Chain approximation of liquid theory and a closure of the BBGKY hierarchy that has been recently introduced by G. Szamel. From both approaches we finally find a set of dynamical Mode-Coupling like equations that are supposed to describe the system in the long time/slow dynamics regime.

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A note on weakly discontinuous dynamical transitions

Cited by 8 publications

References 35 publications

Quasi-equilibrium in glassy dynamics: an algebraic view

Quasi-equilibrium in glassy dynamics: an algebraic view

Universality classes of critical points in constrained glasses

Quasi equilibrium construction for the long time limit of glassy dynamics

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