First-order dynamical phase transition in models of glasses: an approach based on ensembles of histories

By Juan P. Garrahan, Robert L. Jack, V. Lecomte, E. Pitard, K. van Duijvendijk, F. van Wijland. 2008

311 citations recorded by the source corpus.

We investigate the dynamics of kinetically constrained models of glass formers by analysing the statistics of trajectories of the dynamics, or histories, using large deviation function methods. We show that, in general, these models exhibit a first-order dynamical transition between active and inactive dynamical phases. We argue that the dynamical heterogeneities displayed by these systems are a manifestation of dynamical first-order phase coexistence. In particular, we calculate dynamical large deviation functions, both analytically and numerically, for the Fredrickson–Andersen model, the East model, and constrained lattice gas models. We also show how large deviation functions can be obtained from a Landau-like theory for dynamical fluctuations. We discuss possibilities for similar dynamical phase-coexistence behaviour in other systems with heterogeneous dynamics.

Subfields: Condensed Matter Physics, Materials Chemistry, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/862e3ede22636e3031ade6655362478ff4436db0

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In Condensed Matter Physics

In Materials Chemistry

In Statistical and Nonlinear Physics

Citations in the corpus

Theoretical perspective on the glass transition and amorphous materials (2010, background): “The existence of these phase transitions has been proven in simple models (Garrahan et al., 2009) and numerical results for Lennard-Jones model liquids are also consistent with the existence of such a transition (Hedges et al., 2009), which also exists in mean-field models where RFOT theory of Sec.”
Kinetically Constrained Models (2010, unknown): “It is usually argued (Garrahan and Chandler, 2003) that KCMs ought to emerge from some form of local coarse-graining of a microscopic system, but this procedure has not been shown to work just yet (except in highly simplified situations (Garrahan and Newman, 2000; Garrahan et al., 2009b)).”
Aspects of non-equilibrium in classical and quantum systems: Slow relaxation and glasses, dynamical large deviations, quantum non-ergodicity, and open quantum dynamics (2017, methodology): “rrespond to ipping the spins and their associated escape rates, and the factors of n i before the brackets are the kinetic constraints. Let us consider as trajectory observable the dynamical activity [42, 41, 26] (sometimes also termed frenesi [33]) dened as the total number of conguration changes i”