SLOW DROPLET-DRIVEN RELAXATION OF STOCHASTIC ISING-MODELS IN THE VICINITY OF THE PHASE COEXISTENCE REGION

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.