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We introduce a simple nearest-neighbor spin model with multiple metastablephases, the number and decay pathways of which are explicitly controlled by theparameters of the system. With this model we can construct, for example, asystem which evolves through an arbitrarily long succession of metastablephases. We also construct systems in which different phases may nucleatecompetitively from a single initial phase. For such a system, we present ageneral method to extract from numerical simulations the individual nucleationrates of the nucleating phases. The results show that the Ostwald rule, whichpredicts which phase will nucleate, must be modified probabilistically when thenew phases are almost equally stable. Finally, we show that the nucleation rateof a phase depends, among other things, on the number of other phasesaccessible from it.

Competitive nucleation and the Ostwald rule in a generalized Potts model with multiple metastable phases