Communications in Mathematical Physics

, Volume 188, Issue 1, pp 89-119

First online:

Metropolis Dynamics Relaxation via Nucleation and Growth

  • Pouria DehghanpourAffiliated withDepartment of Mathematics, UCLA, Los Angeles, CA 90095, USA
  • , Roberto H. SchonmannAffiliated withDepartment of Mathematics, UCLA, Los Angeles, CA 90095, USA

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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.