METROPOLIS DYNAMICS RELAXATION VIA NUCLEATION AND GROWTH

We consider the Ising model with Metropolis dynamics on Z(2) under a s mall positive external field h. We show that the relaxation time, i.e. , the time it takes for the system to reach the (+)-phase starting fro m all spins-1, scales as e(beta kappa c) as the temperature 1/beta --> 0, where kappa(c) = Gamma+(2-h)/3 and Gamma is the energy of a ''crit ical'' droplet. The factor 1/3 originates from droplet growth and is r elated to the dimension of the lattice, while the term (2-h) is relate d to the rate of growth of highly supercritical droplets.