Tunneling in two dimensions

Giovanni Bellettini, Anna De Masi, Nicolas Dirr, and Errico Presutti

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Submission date: 11. Jul. 2005 (revised version: November 2005)
Pages: 52
published in: Communications in mathematical physics, 269 (2007) 3, p. 715 - 763 
DOI number (of the published article): 10.1007/s00220-006-0143-9
Bibtex
MSC-Numbers: 82C05, 60F10
Keywords and phrases: large deviations, nonlocal evolution equation, tunneling
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Abstract:
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.