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

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 $T\ensuremath{\rightarrow}0$, we provide an exact solution of the resulting coarsening process. The equilibration time exhibits a ``glassy'' divergence ${t}_{\mathrm{eq}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\mathrm{exp}(\mathrm{const}/{T}^{2})$ (popular as an alternative to the Vogel-Fulcher law), while the average domain length grows with a temperature-dependent exponent, $\overline{d}\ensuremath{\sim}{t}^{T\mathrm{ln}2}$. We show that the equilibration time ${t}_{\mathrm{eq}}$ also sets the time scale for the linear response of the system at low temperatures.