Abstract
We show that, under the conditions of the Dobrushin Shlosman theorem for uniqueness of the Gibbs state, the reversible stochastic Ising model converges to equilibrium exponentially fast on the L2 space of that Gibbs state. For stochastic Ising models with attractive interactions and under conditions which are somewhat stronger than Dobrushin’s, we prove that the semi-group of the stochastic Ising model converges to equilibrium exponentially fast in the uniform norm. We also give a new, much shorter, proof of a theorem which says that if the semi-group of an attractive spin flip system converges to equilibrium faster than 1/td where d is the dimension of the underlying lattice, then the convergence must be exponentially fast.
Research supported in part by NSF Grant PHY-8301493A02
Research supported in part by NSF Grant MCS-8310542.
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References
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© 1987 Springer-Verlag New York, Inc.
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Aizenman, M., Holley, R. (1987). Rapid Convergence to Equilibrium of Stochastic Ising Models in the Dobrushin Shlosman Regime. In: Kesten, H. (eds) Percolation Theory and Ergodic Theory of Infinite Particle Systems. The IMA Volumes in Mathematics and Its Applications, vol 8. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8734-3_1
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DOI: https://doi.org/10.1007/978-1-4613-8734-3_1
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