Glassy Time-Scale Divergence and Anomalous Coarsening in a Kinetically Constrained Spin Chain

1999/04/30 by Peter Sollich, M. R. Evans, Martin R Evans · 1 citation
Materials Science · Physics and Astronomy · #Material Dynamics and Properties #Quantum many-body systems #Theoretical and Computational Physics #cond-mat.stat-mech

paper · pdf · doi:10.1103/physrevlett.83.3238

published as Phys. Rev. Lett 83, 3238 (1999) · 4 pages, revtex, includes two eps figures. Proof of energy barrier hierarchy added. Version to be published in Phys Rev Lett

arxiv created 1999/09/23 · openalex publication_date 1999/10/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We analyze the out-of-equilibrium behavior of an Ising spin chain with an asymmetric kinetic constraint after a quench to a low temperature T. In the limit T\ensuremath→0, we provide an exact solution of the resulting coarsening process. The equilibration time exhibits a ``glassy'' divergence t_eq\phantom\rule0ex0ex=\phantom\rule0ex0exexp(const/T²) (popular as an alternative to the Vogel-Fulcher law), while the average domain length grows with a temperature-dependent exponent, d\ensuremath∼t^Tln2. We show that the equilibration time t_eq also sets the time scale for the linear response of the system at low temperatures.

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