Skip to main content
Article thumbnail
Location of Repository

Nonmonotonic behavior in hard-core and Widom-Rowlinson models

By Graham Brightwell, O. Haggström and P. Winkler


We give two examples of nonmonotonic behavior in symmetric systems, exhibiting more than one critical point at which spontaneous symmetry-breaking appears or disappears. The two systems are the hard-core model and the Widom-Rowlinson model, and both examples take place on a variation of the Cayley tree (Bethe lattice) devised by Schonmann and Tanaka. We obtain similar, though less constructive, examples of non-monotonicity via certain local modifications of any graph, e.g. the square lattice, which is known to have a critical point for either model. En route we prove that the Widom-Rowlinson model does behave monotonically on the ordinary Cayley tree, and we obtain an explicit description of its critical behavior there. We conclude with some results about monotonicity of the phase transition phenomenon relative to graph structure

Topics: QA Mathematics
Publisher: Springer
Year: 1999
DOI identifier: 10.1023/A:1004592103315
OAI identifier:
Provided by: LSE Research Online
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • (external link)
  • (external link)
  • Suggested articles

    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.