  Many metastable systems can nucleate to multiple competing stable or
intermediate metastable states. In this work, a Potts model, subject to
external fields, is used to study the competitive nucleation of two phases
attempting to grow on a microscopic impurity. Monte Carlo simulations are used
to calculate the free energy surfaces for the system under different
conditions, where the relative stability of the phases is adjusted by changing
the interaction parameters, and the nucleation rates obtained using
multicomponent transition state theory are compared with the rates measured
using the survival probability method. We find that the two methods predict
similar nucleation rates when the free energy barrier used in the transition
state theory is defined as the work required to form a critical embryo from the
metastable phase. An analysis of the free energy surfaces also reveals that the
competition between the nucleating phases leads to an effective drying of the
impurity which slows down the nucleation rate compared to the single phase
case.
