1987 | OriginalPaper | Chapter
Rapid Convergence to Equilibrium of Stochastic Ising Models in the Dobrushin Shlosman Regime
Authors : M. Aizenman, R. Holley
Published in: Percolation Theory and Ergodic Theory of Infinite Particle Systems
Publisher: Springer New York
Included in: Professional Book Archive
Activate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
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.