Random-cluster representation of the Blume-Capel model

Details Random-cluster representation of the Blume-Capel model Random-cluster representation of the Blume-Capel model

2005-12-22

arxiv.org/abs/math/0512523v1

Mathematics

Probability

Scientific paper

10.1007/s10955-006-9135-6

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 $q\in[1,2]$, and the `edge marginal' when $q\in[1,\oo)$. 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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