Glassy timescale divergence and anomalous coarsening in a kinetically constrained spin chain

Abstract

We analyse 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 \teq=\exp(const/T^2) (popular as an alternative to the Vogel-Fulcher law), while the average domain length grows with a temperature dependent exponent, \dbar ~ t^{T\ln 2}. We show that the equilibration time \teq also sets the timescale for the linear response of the system at low temperatures.

arXiv comment4 pages, revtex, includes two eps figures. Proof of energy barrier hierarchy added. Version to be published in Phys Rev Lett

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