Stability of interfaces and stochastic dynamics in the regime of partial wetting

The goal of this paper is twofold. First, assuming strict convexity of the surface tension, we derive a stability property with respect to the Hausdorff distance of a coarse grained representation of the interface between the two pure phases of the Ising model. This improves the double struck L sign ¹ description of phase segregation. Using this result and an additional assumption on mixing properties of the underlying FK measures, we are then able to derive bounds on the decay of the spectral gap of the Glauber dynamics in dimensions larger or equal to three. These bounds are related to previous results by Martinelli [Ma] in the two-dimensional case. Our assumptions can be easily verified for low enough temperatures and, presumably, hold true in the whole of the phase coexistence region.