  This work extends to dimension $d\geq3$ the main result of Dehghanpour and
Schonmann. We consider the stochastic Ising model on ${\mathbb{Z}}^d$ evolving
with the Metropolis dynamics under a fixed small positive magnetic field $h$
starting from the minus phase. When the inverse temperature $\beta$ goes to
$\infty$, the relaxation time of the system, defined as the time when the plus
phase has invaded the origin, behaves like $\exp({{\beta}{\kappa}_d})$. The
value $\kappa_d$ is equal to
\[{\kappa}_d=\frac{1}{d+1}({\Gamma}_1+\cdots+{\Gamma}_d),\] where ${\Gamma}_i$
is the energy of the $i$-dimensional critical droplet of the Ising model at
zero temperature and magnetic field $h$.
