Disagreement percolation in the study of Markov fields
The influence of the boundary conditions on the state of a Markov lattice field is studied in terms of disagreement percolation. This is done by means of the connection between two Markov field realizations corresponding to different boundary conditions. The constructed connection permit to obtain a new uniqueness condition for Gibbs measure on \(\mathbb{Z}^ d\), \(\sum^ n_{k=0} a^ k/k! < 1/(1 - p_ c)\), where \(p_ c\) is the site percolation threshold for the lattice \(\mathbb{Z}^ d\), \((n + 1)\) is the state number of the considered lattice Gibbs system and \(a = \lambda T\).
scientific article; zbMATH DE number 681381