Rh. Schonmann, SLOW DROPLET-DRIVEN RELAXATION OF STOCHASTIC ISING-MODELS IN THE VICINITY OF THE PHASE COEXISTENCE REGION, Communications in Mathematical Physics, 161(1), 1994, pp. 1-49
We consider the stochastic Ising models (Glauber dynamics) correspondi
ng to the infinite volume basic Ising model in arbitrary dimension d g
reater-than-or-equal-to 2 with nearest neighbor interaction and under
a positive external magnetic field h. Under minimal assumptions on the
rates of flip (so that all the common choices are included), we obtai
n results which state that when the system is at low temperature T, th
e relaxation time when the evolution is started with all the spins dow
n blows up, when h arrow pointing down and to the right 0, as exp(lamb
da(T)/h(d-1)) (the precise results are lower and upper bounds of this
form). Moreover, after a time which does not scale with h and before a
time which also grows as an exponential of a multiple of 1/h(d-1) as
h arrow pointing down and to the right 0, the law of the state of the
process stays, when h is small, close to the minus-phase of the same I
sing model without an external field. These results may be considered
as a partial vindication of a conjecture raised by Aizenman and Lebowi
tz in connection to the metastable behavior of these stochastic Ising
models.