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Slab Percolation and Phase Transitions for the Ising Model

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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 \({\mathbb Z}\) (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.

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Authors and Affiliations

  1. Dipartimento di Matematica “Guido Castelnuovo”, Università di Roma “La Sapienza”., P.le Aldo Moro 2, 00185, Roma, Italia

    Emilio De Santis & Rossella Micieli

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  1. Emilio De Santis
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  2. Rossella Micieli
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Correspondence to Emilio De Santis.

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AMS classification: 60K35, 82B20, 82A25

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De Santis, E., Micieli, R. Slab Percolation and Phase Transitions for the Ising Model. J Stat Phys 122, 59–72 (2006). https://doi.org/10.1007/s10955-005-8086-7

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  • DOI: https://doi.org/10.1007/s10955-005-8086-7

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