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

الأصل · EN

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 (βκd). The value κd is equal to κd=1/d+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.