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

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

2010-07-22

arxiv.org/abs/1007.3824v4

J. Stat. Mech. P01032 (2011)

Physics

Condensed Matter

Statistical Mechanics

17 pages, 7 figures, v2; results have been refined, v3; A figure has been modified, v4; results have been more refined

Scientific paper

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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