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November 2013 Nucleation and growth for the Ising model in $d$ dimensions at very low temperatures
Raphaël Cerf, Francesco Manzo
Ann. Probab. 41(6): 3697-3785 (November 2013). DOI: 10.1214/12-AOP801

Abstract

This work extends to dimension $d\geq3$ the main result of Dehghanpour and Schonmann. We consider the stochastic Ising model on $\mathbb{Z}^{d}$ evolving with the Metropolis dynamics under a fixed small positive magnetic field $h$ starting from the minus phase. When the inverse temperature $\beta$ goes to $\infty$, the relaxation time of the system, defined as the time when the plus phase has invaded the origin, behaves like $\exp(\beta\kappa_{d})$. The value $\kappa_{d}$ is equal to

\[\kappa_{d}=\frac{1}{d+1}(\Gamma_{1}+\cdots+\Gamma_{d}),\]

where $\Gamma_{i}$ is the energy of the $i$-dimensional critical droplet of the Ising model at zero temperature and magnetic field $h$.

Citation

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Raphaël Cerf. Francesco Manzo. "Nucleation and growth for the Ising model in $d$ dimensions at very low temperatures." Ann. Probab. 41 (6) 3697 - 3785, November 2013. https://doi.org/10.1214/12-AOP801

Information

Published: November 2013
First available in Project Euclid: 20 November 2013

zbMATH: 1286.60091
MathSciNet: MR3161463
Digital Object Identifier: 10.1214/12-AOP801

Subjects:
Primary: 60K35, 82C20

Rights: Copyright © 2013 Institute of Mathematical Statistics

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Vol.41 • No. 6 • November 2013
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