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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.

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Authors and Affiliations

  1. Department of Mathematics, UCLA, Los Angeles, CA 90095, USA, , , , , , US

    Pouria Dehghanpour & Roberto H. Schonmann

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  1. Pouria Dehghanpour
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  2. Roberto H. Schonmann
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Received: 11 June 1996 / Accepted: 14 January 1997

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Dehghanpour, P., Schonmann, R. Metropolis Dynamics Relaxation via Nucleation and Growth . Comm Math Phys 188, 89–119 (1997). https://doi.org/10.1007/s002200050158

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  • DOI: https://doi.org/10.1007/s002200050158

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