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Communications in Mathematical Physics

, Volume 55, Issue 1, pp 37–45 | Cite as

In one and two dimensions, every stationary measure for a stochastic Ising Model is a Gibbs state

  • R. A. Holley
  • D. W. Stroock
Article

Abstract

It is shown that one and two dimensional (generalized) stochastic Ising models with finite range potentials have only Gibbs states as their stationary measures. This is true even if the stationary measure or the potential is not translation invariant. This extends previously known results which are restricted to translation invariant stationary measures and potentials. In particular if the potential has only one Gibbs state the stochastic Ising Model must be ergodic.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Stationary Measure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • R. A. Holley
    • 1
  • D. W. Stroock
    • 1
  1. 1.Department of MathematicsUniversity of ColoradoBoulderUSA

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