  A ferromagnetic Ising chain which is endowed with a single-spin-flip Glauber
dynamics is investigated. For an arbitrary annealing protocol, we derive an
exact integral equation for the domain wall density. This integral equation
admits an asymptotic solution in the limit of extremely slow cooling. For
instance, we extract an asymptotic of the density of domain walls at the end of
the cooling procedure when the temperature vanishes. Slow annealing is usually
studied using a Kibble-Zurek argument; in our setting, this argument leads to
approximate predictions which are in good agreement with exact asymptotics.

Statistical Mechanics;Disordered Systems and Neural Networks