Nucleation and growth for the Ising model in $d$ dimensions at very low temperatures
| Autor: | Cerf, Raphaël, Manzo, Francesco |
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| Rok vydání: | 2011 |
| Předmět: | |
| Zdroj: | Annals of Probability 2013, Vol. 41, No. 6, 3697-3785 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1214/12-AOP801 |
| Popis: | 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 $h$. Comment: Published in at http://dx.doi.org/10.1214/12-AOP801 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org) |
| Databáze: | arXiv |
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