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This work extends to dimension $d\geq3$ the main result of Dehghanpour andSchonmann. We consider the stochastic Ising model on ${\mathbb{Z}}^d$ evolvingwith 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 plusphase has invaded the origin, behaves like $\exp({{\beta}{\kappa}_d})$. Thevalue $\kappa_d$ 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 atzero temperature and magnetic field $h$.

Nucleation and growth for the Ising model in $d$ dimensions at very low temperatures