### 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.

Original language | English |
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Pages (from-to) | 715-763 |

Number of pages | 49 |

Journal | Communications in Mathematical Physics |

Volume | 269 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2007 |

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## Cite this

Bellettini, G., De Masi, A., Dirr, N., & Presutti, E. (2007). Tunneling in two dimensions.

*Communications in Mathematical Physics*,*269*(3), 715-763. https://doi.org/10.1007/s00220-006-0143-9