Metropolis Dynamics Relaxation via Nucleation and Growth
- Cite this article as:
- Dehghanpour, P. & Schonmann, R. Comm Math Phys (1997) 188: 89. doi:10.1007/s002200050158
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.