
A Monotonicity Result for Hardcore and WidomRowlinson Models on Certain ddimensional 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 hardcore and
WidomRowlinson 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: 6778
Published on: February 2, 2002

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