Homogeneous and heterogeneous nucleation in the three-state Blume–Capel model

We study metastability in a three-state lattice spin system in presence of zero-boundary condition, which is a relevant choice from the point of view of applications, since it mimics the presence of defects in the system. This problem is studied in the framework of the stochastic Blume–Capel model with Glauber dynamics and it is proven that the presence of zero-boundary conditions changes drastically the metastability scenarios. In particular we show that, depending on the parameters of the model, the stable phase nucleation can be either homogeneous or heterogeneous. Notably, heterogeneous nucleation is proved in the region of the parameter space where the chemical potential is larger than the external magnetic field.