- 93-208 J. van den Berg, C. Maes
- Disagreement percolation in the study of Markov fields
Jul 29, 93
(auto. generated ps),
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Abstract. Recently, one of the authors (vdB) has obtained a uniqueness
Gibbs measures, in terms of disagreement percolation involving two
independent realizations. In the present paper we study the
dependence of Markov fields on boundary conditions by taking a more
suitable coupling. This coupling leads to a new uniqueness condition,
which improves the one mentioned above. We also compare it with the
Dobrushin uniqueness condition.
In the case of the Ising model, our
coupling shares certain properties with the Fortuin-Kasteleyn
it gives an explicit expression of the boundary effect on a certain vertex
in terms of percolation--like probabilities.