Journal of Statistical Physics

, Volume 125, Issue 2, pp 283–316 | Cite as

Random-Cluster Representation of the Blume–Capel Model

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Abstract

The so-called diluted-random-cluster model may be viewed as a random-cluster representation of the Blume–Capel model. It has three parameters, a vertex parameter a, an edge parameter p, and a cluster weighting factor q. Stochastic comparisons of measures are developed for the ‘vertex marginal’ when q ∊ [1,2], and the ‘edge marginal’ when q ∊ [1,∞). Taken in conjunction with arguments used earlier for the random-cluster model, these permit a rigorous study of part of the phase diagram of the Blume–Capel model.

Keywords

Blume–Capel model Ising model Potts model random-cluster model first-order phase transition tri-critical point 
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Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Statistical LaboratoryUniversity of CambridgeCambridgeU.K.

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