We have studied the nucleation in the nearest neighbour ferromagnetic Isingmodel, in different (d) dimensions, by extensive Monte Carlo simulation usingthe heat-bath dynamics. The nucleation time (tau) has been studied as afunction of the magnetic field (h) for various system sizes in differentdimensions (d=2,3,4). The logarithm of the nucleation time is found to beproportional to the power (-(d-1)) of the magnetic field (h) in d dimensions.The size dependent crossover from coalescence to nucleation regime is observedin all dimensions. The distribution of metastable lifetimes are studied in bothregions. The numerical results are compared and found to be consistent with theclassical theoretical predictions. In two dimensions, we have also studied thedynamical response to a sinusoidally oscillating magnetic field. The reversaltime is studied as a function of the inverse of the coercive field. Theapplicability of the classical nucleation theory to study the hysteresis andcoercivity has been discussed.
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