Glassy dynamics of kinetically constrained models
Felix Ritort,Peter Sollich +1 more
TL;DR: In this article, the authors review the use of kinetically constrained models (KCMs) for the study of dynamics in glassy systems, including spin-facilitated (Ising) models, constrained lattice gases, models inspired by cellular structures such as soap froths, models obtained via mappings from interacting systems without constraints, and related models such as urn, oscillator, tiling and needle models.
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Abstract: We review the use of kinetically constrained models (KCMs) for the study of dynamics in glassy systems. The characteristic feature of KCMs is that they have trivial, often non-interacting, equilibrium behaviour but interesting slow dynamics due to restrictions on the allowed transitions between configurations. The basic question which KCMs ask is therefore how much glassy physics can be understood without an underlying ‘equilibrium glass transition’. After a brief review of glassy phenomenology, we describe the main model classes, which include spin-facilitated (Ising) models, constrained lattice gases, models inspired by cellular structures such as soap froths, models obtained via mappings from interacting systems without constraints, and finally related models such as urn, oscillator, tiling and needle models. We then describe the broad range of techniques that have been applied to KCMs, including exact solutions, adiabatic approximations, projection and mode-coupling techniques, diagrammatic approaches and mappings to quantum systems or effective models. Finally, we give a survey of the known results for the dynamics of KCMs both in and out of equilibrium, including topics such as relaxation time divergences and dynamical transitions, nonlinear relaxation, ageing and effective temperatures, cooperativity and dynamical heterogeneities, and finally non-equilibrium stationary states generated by external driving. We conclude with a discussion of open questions and possibilities for future work.
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Citations
Exact solution of a jamming transition: Closed equations for a bootstrap percolation problem
TL;DR: A bootstrap percolation model is able to solve one such model in two dimensions exactly, exhibiting the precise evolution of the jamming correlations on approach to arrest and the nature of these correlations and the method devised to solve the problem are quite general.
Decoupling of self-diffusion and structural relaxation during a fragile-to-strong crossover in a kinetically constrained lattice gas.
TL;DR: It is shown that a fragile-to-strong crossover can be modeled by a union of two kinetically constrained lattice gas models and that, for this model, the variation of the product of the self-diffusion constant and the structural relaxation time is non-monotonic with temperature as a result of the crossover.
Size-stretched exponential relaxation in a model with arrested states.
TL;DR: Interestingly, the stretched exponential form of the autocorrelation function of a single typical sample in the steady state differs markedly from that averaged over an ensemble of initial conditions resulting from different quenches; the latter shows a slow power-law decay at large times.
Universality for critical KCM: infinite number of stable directions
TL;DR: In this article, the authors established the universality classes of critical KCM and determined within each class the critical exponent of the infection time as well as of the spectral gap, and showed that for critical models with an infinite number of stable directions this exponent is twice the one of their bootstrap percolation counterpart.
Cooperative transport with selective kinetic constraints.
TL;DR: In this article, a family of cooperative exclusion processes whose microscopic dynamics is governed by selective kinetic constraints is introduced and studied, which display, in sharp contrast to the simple symmetric exclusion process, density profiles that can be concave, convex or both, depending on the density of boundary particle reservoirs.
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