A kinetically constrained model on a triangular ladder is shown to have mean-field diffusion coefficient D = 3(1 - ρ), with a jamming transition at density ρ = 2/3.
Theory of Kinetically-Constrained-Models Dynamics
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The mean-field theory of Kinetically-Constrained-Models is developed by considering the Fredrickson-Andersen model on the Bethe lattice. Using certain properties of the dynamics observed in actual numerical experiments we derive asymptotic dynamical equations equal to those of Mode-Coupling-Theory. Analytical predictions obtained for the dynamical exponents are successfully compared with numerical simulations in a wide range of models, including the case of generic values of the connectivity and the facilitation, random pinning and fluctuating facilitation. The theory is thus validated for both continuous and discontinuous transitions and also in the case of higher order critical points characterized by logarithmic decays.
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A kinetically constrained model exhibiting non-linear diffusion and jamming
A kinetically constrained model on a triangular ladder is shown to have mean-field diffusion coefficient D = 3(1 - ρ), with a jamming transition at density ρ = 2/3.