Random-Cluster Representation of the Blume–Capel Model |
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Authors: | B T Graham G R Grimmett |
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Institution: | (1) Statistical Laboratory, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WB, U.K. |
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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.
Mathematics Subject Classification (2000): 82B20, 60K35. |
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Keywords: | Blume– Capel model Ising model Potts model random-cluster model first-order phase transition tri-critical point |
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