First steps of a nucleation theory in disordered systems

We devise a field theoretical formalism for a microscopic theory of nucleation processes and phase coexistence in finite dimensional glassy systems. We study disordered p -spin models with large but finite range of interaction. We work in the framework of glassy effective potential theory which in the mean field is a non-convex, two-minimum function of the overlap. We associate metastability and phase coexistence with the existence of space inhomogeneous solutions of suitable field equations and we study the simplest of such solutions.