Slab Percolation and Phase Transitions for the Ising Model |
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Authors: | Emilio De Santis Rossella Micieli |
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Affiliation: | (1) Dipartimento di Matematica “Guido Castelnuovo”, Università di Roma “La Sapienza”., P.le Aldo Moro 2, 00185 Roma, Italia |
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Abstract: | We prove, using the random-cluster model, a strict inequality between site percolation and magnetization in the region of phase transition for the d-dimensional Ising model, thus improving a result of [5]. We extend this result also at the case of two plane lattices (slabs) and give a characterization of phase transition in this case. The general case of N slabs, with N an arbitrary positive integer, is partially solved and it is used to show that this characterization holds in the case of three slabs with periodic boundary conditions. AMS classification: 60K35, 82B20, 82A25 |
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Keywords: | Percolation infinite clusters magnetization Gibbs measure random-cluster measure |
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