Communications in Mathematical Physics

, Volume 188, Issue 1, pp 89–119

Metropolis Dynamics Relaxation via Nucleation and Growth

Authors

  • Pouria Dehghanpour
    • Department of Mathematics, UCLA, Los Angeles, CA 90095, USA
  • Roberto H. Schonmann
    • Department of Mathematics, UCLA, Los Angeles, CA 90095, USA

DOI: 10.1007/s002200050158

Cite this article as:
Dehghanpour, P. & Schonmann, R. Comm Math Phys (1997) 188: 89. doi:10.1007/s002200050158

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.

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© Springer-Verlag Berlin Heidelberg 1997