Homogeneous and heterogeneous nucleation in Ising models

Nucleation in Ising models with short and long-range interactions is investigated via Monte Carlo simulations. The systems are quenched into a metastable region either near the coexistence curve where nucleation is classical or near the spinodal where nucleation is non-classical. The spinodal is defined only in the mean-field limit and is replaced by a pseudospinodal in long but finite-range interaction systems. Several aspects of nucleation are discussed: the thermodynamical interpretation of the pseudospinodal, the nucleation mechanism near the spinodal, and heterogeneous nucleation, nucleation in the presence of impurities.; I find that the pseudospinodal in the Ising model has a theoretical foundation described by the leading zero of the partition function expressed in terms of complex magnetic field and complex temperature. This result is analogous to the behavior of the zeros of the partition function at the Ising critical point for finite systems, and provides more evidence that the spinodal for finite systems is observable.; Because the spinodal is a critical point, nucleation near the spinodal occurs very differently compared to nucleation near the coexistence curve. The nucleating droplet forms by the coalescence of ramified and diffuse droplets. I find that as the system becomes more mean-field, the number of coalescing clusters and the time over which they merge increases.; Heterogeneous nucleation is simulated in Ising models with short and long-range interactions by adding fixed impurities and walls. Two experimentally interesting quantities are measured: the probability of nucleation occurring on the impurity (heterogeneously) or at some other location (homogeneously), and the survival curves which shows the probability of the system remaining in a metastable state as a function of the quench depth.; The probability of nucleation occurring heterogeneously or homogeneously depend strongly on the quench depth, the size of the impurity, and the interaction range. The survival probabilities are also measured for these systems with and without impurities and walls. For short-range interactions I find that as the impurity size is increased, the slope of the survival curve becomes steeper (with the exception of the case where only one spin is fixed). For long-range systems no change is observed in the slopes for the impurity sizes studied.