Exponential Relaxation of Glauber Dynamics with Some Special Boundary Conditions |
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Authors: | Roberto H Schonmann Nobuo Yoshida |
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Institution: | (1) Mathematics Department, UCLA, Los Angeles, CA 90024, USA. E-mail: rhs@math.ucla.edu, US;(2) Division of Mathematics, Graduate School of Science, Kyoto University, Kyoto 606-01, Japan. E-mail: nobuo@kusm.kyoto-u.ac.jp, JP;(3) Mathematics Department, 2-101, MIT, Cambridge, MA 02139, USA. E-mail: nobuo@math.mit.edu, US |
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Abstract: | We consider attractive finite-range Glauber dynamics and show that if a certain mixing condition is satisfied, then the system
evolving on arbitrary subsets of the lattice, with appropriate boundary conditions, converges to equilibrium exponentially
fast, in the uniform sense, uniformly over the subsets of the lattice. This result applies, for instance, to the ferromagnetic
nearest neighbor Ising model in the so-called “Basuev region,” where complete analyticity is expected to fail.
Technically the result in this paper is an extension of a result of Martinelli and Olivieri, who proved that under a weaker
form of mixing the infinite system approaches equilibrium exponentially fast.
Conceptually this paper may be seen as a step towards developing and exploiting a restricted notion of complete analyticity
in which the boundary conditions, rather than the shapes of the regions under consideration, are being restricted.
Received: 24 May 1996 / Accepted: 24 May 1996 |
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