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 $T\to 0$, we provide an exact solution of the resulting coarsening process. The equilibration time exhibits a “glassy” divergence $t_{\mathrm{eq}}=\exp \left(\mathrm{const}/T^2\right)$ (popular as an alternative to the Vogel-Fulcher law), while the average domain length grows with a temperature-dependent exponent, $\overline{d}\sim t^{T\ln 2}$. We show that the equilibration time $t_{\mathrm{eq}}$ also sets the time scale for the linear response of the system at low temperatures.

• Received 9 April 1999

DOI:https://doi.org/10.1103/PhysRevLett.83.3238