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

This work extends to dimension d.3 the main result of Dehghanpour and Schonmann. We consider the stochastic Ising model on Zd evolving with the Metropolis dynamics under a fixed small positive magnetic field h starting from the minus phase. When the inverse temperature . goes to ., the relaxation time of the system, defined as the time when the plus phase has invaded the origin, behaves like exp(..d). The value .d is equal to .d=1d+1(.1+.+.d), where .i is the energy of the i-dimensional critical droplet of the Ising model at zero temperature and magnetic field h.