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 Electronic Communications in Probability > Vol. 7 (2002) > Paper 7 open journal systems 


A Monotonicity Result for Hard-core and Widom-Rowlinson Models on Certain d-dimensional Lattices

Olle Häggström, Chalmers University of Technology and Goteborg University


Abstract
For each $dgeq 2$, we give examples of $d$-dimensional periodic lattices on which the hard-core and Widom-Rowlinson models exhibit a phase transition which is monotonic, in the sense that there exists a critical value $lambda_c$ for the activity parameter $lambda$, such that there is a unique Gibbs measure (resp. multiple Gibbs measures) whenever $lambda$ is less than $lambda_c$ (resp. $lambda$ greater than $lambda_c$). This contrasts with earlier examples of such lattices, where the phase transition failed to be monotonic. The case of the cubic lattice $Z^d$ remains an open problem.


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Pages: 67-78

Published on: February 2, 2002


Bibliography
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Electronic Communications in Probability. ISSN: 1083-589X