Tunneling in Two Dimensions

Bellettini, G., De Masi, A., Dirr, Nicolas P. ORCID: https://orcid.org/0000-0003-3634-7367 and Presutti, E. 2006. Tunneling in Two Dimensions. Communications in Mathematical Physics 269 (3) , pp. 715-763. 10.1007/s00220-006-0143-9

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Abstract

Tunneling 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, [9]. The spatial domain is a two-dimensional square of side L with reflecting boundary conditions. For L large enough the penalty for tunneling 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 tunneling. In a final section (Sect. 11), we extend the results to d = 3 but their validity in d > 3 is still open.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Schools > Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Springer
ISSN:	0010-3616
Last Modified:	18 Oct 2022 13:13
URI:	https://orca.cardiff.ac.uk/id/eprint/13066

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