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

TL;DR

This paper provides an exact analysis of the out-of-equilibrium dynamics of a kinetically constrained Ising spin chain, revealing glassy divergence of equilibration time and anomalous domain growth at low temperatures.

Contribution

It offers an exact solution for the coarsening process in a kinetically constrained spin chain at zero temperature, highlighting glassy dynamics and anomalous coarsening behavior.

Findings

Equilibration time diverges as rac{rac{1}{T^2}}

Average domain length grows with a temperature-dependent exponent

Linear response timescale matches equilibration time at low T

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.