Calculus of Variations and Geometric Measure Theory
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G. Bellettini - A. De Masi - N. Dirr - E. Presutti

Tunnelling in two dimensions

created by belletti on 02 Nov 2005
modified on 13 Dec 2006


Accepted Paper

Inserted: 2 nov 2005
Last Updated: 13 dec 2006

Journal: Comm. Math. Phys.
Year: 2006


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.

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