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Analysis and Stochastics of Growth Processes and Interface Models$
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Peter Mörters, Roger Moser, Mathew Penrose, Hartmut Schwetlick, and Johannes Zimmer

Print publication date: 2008

Print ISBN-13: 9780199239252

Published to Oxford Scholarship Online: September 2008

DOI: 10.1093/acprof:oso/9780199239252.001.0001

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Switching Paths for Ising Models with Long-Range Interaction

Switching Paths for Ising Models with Long-Range Interaction

Chapter:
(p.244) 11 Switching Paths for Ising Models with Long-Range Interaction
Source:
Analysis and Stochastics of Growth Processes and Interface Models
Author(s):

Nicolas Dirr

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199239252.003.0011

The chapter discusses a multiscale model for a two-phases material. The model is a stochastic process on the finest scale. The effective behaviour on larger scales is governed by deterministic nonlinear evolution equations. Due to the stochasticity on the finest scale, deviations from these limit evolution laws can happen with small probability. The chapter describes the most likely among those deviations in two situations: (i) the switching from one stable equilibrium of the evolution equation to another one, (ii) enforced, fast motion on a manifold of stationary solutions. This chapter is based on joint work with Giovanni Bellettini, Anna DeMasi and Errico Presutti.

Keywords:   Ising model, two-phases material, long-range interaction, switching, enforced motion

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