Shapes of growing droplets -- a model of escape from a metastable phase (Q1897025)

The aim of the present paper is to discuss the shape of a growing crystal modeled by an Ising model with ferromagnetic nearest neighbor and next nearest neighbour interactions in the presence of a small positive external field. A detailed description of the escape pattern in the asymptotic region of vanishing temperatures is presented. The main result (Theorem 3) says that, for a Glauber dynamics, the growth of subcritical crystals is through a sequence of particular shapes that significantly differ from the equilibrium Wulff octagons.