Abstract
We study the random-cluster model on a homogeneous tree, and show that the following three conditions are equivalent for a random-cluster measure: quasilocality, almost sure quasilocality, and the almost sure nonexistence of infinite clusters. As a consequence of this, we find that the plus measure for the Ising model on a tree at sufficiently low temperatures can be mapped, via a local stochastic transformation, into a measure which fails to be almost surely quasilocal.
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Communicatd by A. C. D. van Enter
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Häggström, O. Almost sure quasilocality fails for the random-cluster model on a tree. J Stat Phys 84, 1351–1361 (1996). https://doi.org/10.1007/BF02174134
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DOI: https://doi.org/10.1007/BF02174134