94-283 G.Giacomin, J.L.Lebowitz, C.Maes

Agreement percolation and phase coexistence in some Gibbs systems (98K, AmsTex 2.1, Amsppt 2.1a) Sep 10, 94

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Abstract. We extend some relations between percolation and the dependence of Gibbs states on boundary conditions known for Ising ferromagnets to other systems and investigate their general validity: percolation is defined in terms of the agreement of a configuration with one of the ground states of the system. This extension is studied via examples and counterexamples, including the antiferromagnetic Ising and hard-core models on bipartite lattices, Potts, many layered Ising and continuum Widom-Rowlinson (WR) models. In particular our results on the hard square lattice model make rigorous observations made in Hu and Mak (1989) and (1990) on the basis of computer simulations. Moreover we observe that the (naturally defined) clusters of the WR model play (for the WR model itself) the same role that the clusters of the Fortuin-Kasteleyn measure play for the ferromagnetic Potts models. The phase transition and percolation in this system can be mapped into the corresponding liquid-vapor transition of a one component fluid.

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