Systematic perturbation approach for a dynamical scaling law in a kinetically constrained spin model
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.
Cite
@article{arxiv.1007.3824,
title = {Systematic perturbation approach for a dynamical scaling law in a kinetically constrained spin model},
author = {Hiroki Ohta},
journal= {arXiv preprint arXiv:1007.3824},
year = {2015}
}
Comments
17 pages, 7 figures, v2; results have been refined, v3; A figure has been modified, v4; results have been more refined