Slow Dynamics for the Dilute Ising Model in the Phase Coexistence Region

In this paper we consider the Glauber dynamics for a disordered ferromagnetic Ising model, in the region of phase coexistence. It was conjectured several decades ago that the spin autocorrelation decays as a negative power of time [Huse and Fisher, in Phys Rev B 35(13):6841–6846, 1987]. We confirm this behavior by establishing a corresponding lower bound in any dimensions d ≥ 2, together with an upper bound when d = 2. Our approach is deeply connected to the Wulff construction for the dilute Ising model. We consider initial phase profiles with a reduced surface tension on their boundary and prove that, under mild conditions, those profiles are separated from the (equilibrium) pure plus phase by an energy barrier.