Nucleation and growth for the Ising model in d dimensions at very low temperatures

Raphaël Cerf ^[1] ; Francesco Manzo ^[2]
1. [1] Université Paris Sud et IUF
2. [2] Università di Roma Tre
Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 41, Nº. 6, 2013, págs. 3697-3785
Idioma: inglés
DOI: 10.1214/12-AOP801
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Resumen
- This work extends to dimension d≥3 the main result of Dehghanpour and Schonmann. We consider the stochastic Ising model on Zd evolving with the Metropolis dynamics under a fixed small positive magnetic field h starting from the minus phase. When the inverse temperature β goes to ∞, the relaxation time of the system, defined as the time when the plus phase has invaded the origin, behaves like exp(βκd). The value κd is equal to κd=1d+1(Γ1+⋯+Γd), where Γi is the energy of the i-dimensional critical droplet of the Ising model at zero temperature and magnetic field h.