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The random-cluster model on a homogeneous tree
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  • Published: June 1996

The random-cluster model on a homogeneous tree

  • Olle Häggström1 

Probability Theory and Related Fields volume 104, pages 231–253 (1996)Cite this article

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Summary

The random-cluster model on a homogeneous tree is defined and studied. It is shown that for 1≦q≦2, the percolation probability in the maximal random-cluster measure is continuous inp, while forq>2 it has a discontinuity at the critical valuep=p c (q). It is also shown that forq>2, there is nonuniqueness of random-cluster measures for an entire interval of values ofp. The latter result is in sharp contrast to what happens on the integer lattice Zd.

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Authors and Affiliations

  1. Department of Mathematics, Chalmers University of Technology, S-412 96, Göteborg, Sweden

    Olle Häggström

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  1. Olle Häggström
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Research partially supported by a grant from the Royal Swedish Academy of Sciences

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Häggström, O. The random-cluster model on a homogeneous tree. Probab. Th. Rel. Fields 104, 231–253 (1996). https://doi.org/10.1007/BF01247839

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  • Received: 28 February 1995

  • Revised: 19 July 1995

  • Issue Date: June 1996

  • DOI: https://doi.org/10.1007/BF01247839

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Mathematics Subject Classification (1991)

  • 60K35
  • 82B20
  • 05C80
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