Switching Paths for Ising Models with Long-Range Interaction

Nicolas Dirr

doi:10.1093/acprof:oso/9780199239252.003.0011

Switching Paths for Ising Models with Long-Range Interaction

Nicolas Dirr

University of Bath

Research output: Chapter or section in a book/report/conference proceeding › Chapter or section

Abstract

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.

Original language	English
Title of host publication	Analysis and Stochastics of Growth Processes and Interface Models
Editors	Peter Morters , Matthew Penrose , Hartmut Schwetlick , Johanes Zimmer
Publisher	Oxford University Press
ISBN (Print)	9780199239252
DOIs	https://doi.org/10.1093/acprof:oso/9780199239252.003.0011
Publication status	Published - 2008

Keywords

Enforced motion
Ising model
Long-range interaction
Switching
Two-phases material

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10.1093/acprof:oso/9780199239252.003.0011

Cite this

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abstract = "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.",

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AB - 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.

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Switching Paths for Ising Models with Long-Range Interaction

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Keywords

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