Percolation and Gibbs states multiplicity for ferromagnetic Ashkin-Teller models on

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, , Citation L Chayes et al 1998 J. Phys. A: Math. Gen. 31 9055 DOI 10.1088/0305-4470/31/45/005

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1 Department of Mathematics, University of California, Los Angeles, CA 90095-1555, USA

Dates

  1. Received 16 September 1997

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0305-4470/31/45/9055

Abstract

For a region of the nearest-neighbour ferromagnetic Ashkin-Teller spin systems on , we characterize the existence of multiple Gibbs states via percolation. In particular, there are multiple Gibbs states if and only if there exists percolation of any of the spin types (i.e. the magnetized states are characterized by percolation of the dominant species). This result was previously known only for the Potts models on .

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