  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 sharp estimates on the
distribution of the times of 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.
