Abstract

Random-Cluster Representation of the Ashkin-Teller Model C.-E. Pfister and Y. Velenik J. Stat. Phys. 88, 1295-1331 (1997). We show that a class of spin models, containing the Ashkin-Teller model, admits a generalized random-cluster (GRC) representation. Moreover we show that basic properties of the usual representation, such as FKG inequalities and comparison inequalities, still hold for this generalized random-cluster model. Some elementary consequences are given. We also consider the duality transformations in the spin representation and in the GRC model and show that they commute. Key words: Ashkin-Teller model, percolation, random-cluster, duality, FKG, comparison inequalities. Files: PDF, bibtex