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Blocking and Dimer Processes on the Cayley Tree

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Abstract

We show that the equilibrium distribution for the dimer process on the finite Cayley tree tends to a translation invariant limit as the size of the tree tends to infinity. The same is true for the blocking process except when there is a phase transition, in which case there are two limits, each a one-step translation of the other. We also find correlations for occupation probabilities.

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Authors and Affiliations

  1. Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático, Universidad de Chile, Av. Blanco Encalada 2120, 837-0459, Santiago, Chile

    Raul Gouet

  2. School of Mathematical Sciences, Monash University, 3800, Victoria, Australia

    Aidan Sudbury

Authors
  1. Raul Gouet
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  2. Aidan Sudbury
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Correspondence to Raul Gouet.

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Gouet, R., Sudbury, A. Blocking and Dimer Processes on the Cayley Tree. J Stat Phys 130, 935–955 (2008). https://doi.org/10.1007/s10955-007-9451-5

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  • DOI: https://doi.org/10.1007/s10955-007-9451-5

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