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Tunneling in two dimensions
Giovanni Bellettini, Anna De Masi, Nicolas Dirr and Errico Presutti
Tunnelling is studied here as a variational problem formulated in terms of a functional which approximates the rate function for large deviations in Ising systems with Glauber dynamics and Kac potentials. The spatial domain is a two-dimensional square of side $L$ with reflecting boundary conditions. For $L$ large enough the penalty for tunnelling from the minus to the plus equilibrium states is determined. Minimizing sequences are fully characterized and shown to have approximately a planar symmetry at all times, thus departing from the Wulff shape in the initial and final stages of the tunnelling.