Glassy dynamics of kinetically constrained models

By Felix Ritort, Peter Sollich. 2002

674 citations recorded by the source corpus.

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.

Subfields: Condensed Matter Physics, Materials Chemistry, Physical and Theoretical Chemistry

View Paper: https://www.semanticscholar.org/paper/85c63055c78d64200501e3abc6d623dc4e6ce2e6

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In Condensed Matter Physics

In Materials Chemistry

In Physical and Theoretical Chemistry

Citations in the corpus

Excitations Are Localized and Relaxation Is Hierarchical in Glass-Forming Liquids (2011, background): “…Ann Arbor MI, 48109-2136 and Department of Materials Science Engineering, University of Michigan, Ann Arbor MI, 48109-2136 David Chandler† Department of Chemistry, University of California, Berkeley CA, 94720 (Dated: January 31, 2013) For several atomistic models of glass formers, at…”
Ergodicity Breaking Arising from Hilbert Space Fragmentation in Dipole-Conserving Hamiltonians (2019, background): “[96] F.”
Colloquium : The glass transition and elastic models of glass-forming liquids (2006, background): “…2005 ; models with trivial thermodynamics, but nontrivial dynamics Fredrickson, 1988; Pitts, Young, and Andersen, 2000; Garrahan and Chandler, 2002; Ritort and Sollich, 2003; Pedersen et al., 2006 ; the random first-order transition theory Kirkpatrick, Thirumalai, and Wolynes, 1989; Xia and…”
Melting artificial spin ice (2011, background): “In general, the absence of unique ground states [8] and the presence of kinetic constraints [17] make the study of excitations extremely important.”
Hilbert Space Fragmentation and Commutant Algebras (2021, background): “In the former case, all operators in the commutant are diagonal in the product state basis, and this type of fragmentation can also occur in constrained classical systems with the same set of transition rules [48], where the phenomenon is an example of “reducibility” [29].”
Kinetically Constrained Models (2010, positive): “…were proposed in the 80s (Fredrickson and Andersen, 1984) and 90s (Eisinger and Jäckle, 1991), with some work continuing into the present decade (Ritort and Sollich, 2003), particularly regarding the non-equilibrium behaviour (see Section 1.4.3) and detailed comparisons with glass…”
Aspects of non-equilibrium in classical and quantum systems: Slow relaxation and glasses, dynamical large deviations, quantum non-ergodicity, and open quantum dynamics (2017, background): “The need for a neighbouring excitation to allow motion is often called facilitation [30, 8, 29].”