P. Dehghanpour et Rh. Schonmann, METROPOLIS DYNAMICS RELAXATION VIA NUCLEATION AND GROWTH, Communications in Mathematical Physics, 188(1), 1997, pp. 89-119
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.