We use the zero-temperature random-field Ising model to study hysteretic behavior at first-order phase transitions. Sweeping the external field through zero, the model exhibits hysteresis, the return-point memory effect, and avalanche fluctuations.There is a critical value of disorder at which a jump in the magnetization (corresponding to an infinite avalanche) first occurs. We study the universal behavior at this critical point using mean-field theory, and also present preliminary results of numerical simulations in three dimensions.

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We use molecular dynamics to study the nucleation of AgBr in water. After first testing our Born–Mayer–Huggins potentials for Ag+ and Br− by looking at bulk AgBr and at AgBr clusters in vacuo, we consider small numbers of Ag+ and Br− ions immersed in water. The system shows the expected qualitative features of nucleation form solution, including a critical cluster size that decreases with increasing concentration. However, we find that for cluster sizes at least as large as Ag18Br18, the most stable cluster is disordered. This is in stark contrast to clusters in vacuo where clusters as small as Ag4Br4 from ordered fragments of the lattice. These results lend some support to the conjecture that nucleation of crystals from solution is a two-stage process with the first stage consisting of the formation of disordered clusters of solute and the second stage involving the nucleation of a crystal from this solute “melt.”

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