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 t(eq) = exp(const/T-2) (popular as an alternative to the Vogel-Fulcher law), while the average domain length grows with a temperature-dependent exponent, (d) over bar similar to t(T ln2). We show that the equilibration time t(eq) also sets the time scale for the linear response of the system at low temperatures.