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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.

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  1. Statistical Laboratory, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WB, U.K.

    B. T. Graham & G. R. Grimmett

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  1. B. T. Graham
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  2. G. R. Grimmett
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Correspondence to G. R. Grimmett.

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Mathematics Subject Classification (2000): 82B20, 60K35.

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Graham, B.T., Grimmett, G.R. Random-Cluster Representation of the Blume–Capel Model. J Stat Phys 125, 283–316 (2006). https://doi.org/10.1007/s10955-006-9135-6

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