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arXiv · 1007.3824

Systematic perturbation approach for a dynamical scaling law in a kinetically constrained spin model

Hiroki Ohta
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Abstract

The dynamical behaviours of a kinetically constrained spin model (Fredrickson-Andersen model) on a Bethe lattice are investigated by a perturbation analysis that provides exact final states above the nonergodic transition point. It is observed that the time-dependent solutions of the derived dynamical systems obtained by the perturbation analysis become systematically closer to the results obtained by Monte Carlo simulations as the order of a perturbation series is increased. This systematic perturbation analysis also clarifies the existence of a dynamical scaling law, which provides a implication for a universal relation between a size scale and a time scale near the nonergodic transition.

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Hiroki Ohta. 2010-12-29. Systematic perturbation approach for a dynamical scaling law in a kinetically constrained spin model. https://doi.org/10.1088/1742-5468%2F2011%2F01%2Fp01032

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