Ising Droplets, Nucleation, and Stretched Exponential Relaxation

The standard Ising model in two and three dimensions was simulated with Metropolis-Glauber kinetics on the Intel Hypercube with 32 MIMD processors of i860 type, each with 16 megabytes of distributed memory, and on 8 such processors of the Alliant FX with shared memory. The nucleation time in reverse magnetic fields h. was found to increase as 1/h 2 in three dimensions, for times up to millions of iterations. The relaxation towards the equilibrium spontaneous magnetization was a simple exponential in three dimensions and a stretched exponential in two below the critical temperature; its power-law decay at the critical point lead to z=2.18(d=2) and =2.09 (d=3). The Becker-Döring equation for the growth of microdroplets leads at the critical temperature to a growth rate vanishing with some power of the time.