, Volume 188, Issue 1, pp 89-119

Metropolis Dynamics Relaxation via Nucleation and Growth

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Abstract:

We consider the Ising model with Metropolis dynamics on under a small positive external field h. We show that the relaxation time, i.e., the time it takes for the system to reach the (+)-phase starting from all spins -1, scales as as the temperature , where and is the energy of a “critical” droplet. The factor originates from droplet growth and is related to the dimension of the lattice, while the term (2-h) is related to the rate of growth of highly supercritical droplets.

Received: 11 June 1996 / Accepted: 14 January 1997