Slow dynamics for the dilute Ising model in the phase coexistence region

Abstract

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, Phys. Rev. B, 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.

44 pages, 6 figures

References in corpus (3)

• On the mixing time of the 2D stochastic Ising model with "plus" boundary conditions at low temperature
• Surface tension in the dilute Ising model. The Wulff construction
• A coarse graining for the Fortuin-Kasteleyn measure in random media