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Kinetically constrained spin models

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SNAW01 - Graph limits and statistics

We shall discuss kinetically constrained spin models (KCSM), a class ofinteracting particle systems which have been introduced in physics liter-ature to model liquid-glass and more general jamming transitions. Theevolution of KCSM follows a continuous time Markov process whoseelementary moves are birth and death of particles. The key feature isthat a move occurs only if the con guration satis es a local constraint.These constraints induce the existence of clusters of blocked particles,the occurrence of several invariant measures and ergodicity breakingtransitions. We shall present some results concerning the identi cationof the ergodic regime and the exponential convergence to equilibriumin this regime. After establishing a connection with monotone cellu-lar automata of bootstrap percolation type, we shall conclude our talkwith a discussion of a particular KCSM for which the correspondingcellular automaton has a peculiar discontinuous percolation transition.

This talk is part of the Isaac Newton Institute Seminar Series series.

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