English

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

Statistical Mechanics 2015-05-19 v4 Soft Condensed Matter

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.

Keywords

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

R2 v1 2026-06-21T15:51:22.525Z