Kinetically constrained models

Kinetically constrained models are stochastic systems whose local transitions are allowed only when specified neighboring configurations meet kinetic rules. They explain slow relaxation and dynamical arrest without requiring complex static interactions.

Fredrickson–Andersen model: A lattice model in which a spin can flip only when enough neighboring spins are excited. Its facilitation rule is a canonical example of constraints generating glassy relaxation.
Markov process: A stochastic process whose future state depends on its present state rather than its full history. Constrained models commonly specify transitions as a continuous-time Markov process.
Glass transition: The transformation of a supercooled liquid into a rigid glass without crystallization. Kinetically constrained models reproduce aspects of glassy slowdown without a thermodynamic transition.
Facilitated spin model: A spin system in which local changes depend on the states of neighboring spins. This broader model family overlaps strongly with kinetically constrained models but need not use the same formal restrictions.
East model: A one-dimensional spin model where a site can flip only if its left neighbor is excited. Its directional constraint produces hierarchical relaxation times.
Detailed balance: A condition on transition rates that makes equilibrium probability flow balance between every pair of states. Many models impose it while separately restricting which transitions are possible.
Supercooled liquid: A liquid cooled below its melting point without crystallizing. Its rapidly increasing relaxation time is a central phenomenon these models seek to explain.
Random energy model: A disordered energy-landscape model in which configurations have independent random energies. It explains glassy behavior through landscape statistics rather than explicit local kinetic rules.
Dynamic facilitation theory: A framework explaining glassy dynamics through mobile excitations that facilitate motion nearby. It interprets constrained transitions as the propagation of mobility.
Kinetic constraint: A rule that permits a state transition only when nearby degrees of freedom satisfy a specified condition. It is the defining local ingredient distinguishing these models from ordinary stochastic dynamics.

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Glassy systemsBroader topic: It demonstrates that glassy behavior need not originate in a complex energy landscape.