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

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→0, we provide an exact solution of the resulting coarsening process. The equilibration time exhibits a ``glassy'' divergence teq0ex0ex=0ex0exexp(const/T²) (popular as an alternative to the Vogel-Fulcher law), while the average domain length grows with a temperature-dependent exponent, d̄~tTln2. We show that the equilibration time teq also sets the time scale for the linear response of the system at low temperatures.