A. Bovier, F. Manzo
Metastability in Glauber Dynamics in the Low-Temperature limit:
Beyond Exponential Asymptotics
(55K, LaTeX)
ABSTRACT. We consider Glauber dynamics of classical spin systems of Ising type
in the limit when the temperature tends to zero in finite volume. We
show that information on the structure of the most profound minima and
the connecting saddle points of the Hamiltonian can be translated into
{\it sharp} estimates on the distribution of the times of {\it
metastable } transitions between such minima as well as the low lying
spectrum of the generator. In contrast with earlier results on
such problems, where only the asymptotics of the exponential rates is
obtained, we compute the precise pre-factors up to multiplicative
errors that tend to 1 as $T\downarrow 0$. As an example we treat the
nearest neighbor Ising model on the 2 and 3 dimensional square
lattice. Our results improve considerably earlier estimates obtained
by Neves-Schonmann and
Ben Arous-Cerf . Our results employ the methods
introduced by Bovier, Eckhoff, Gayrard, and Klein.