 |
|
|
| | | | | |
|
|
|
|
|
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.
|
Full text: PDF
Pages: 67-78
Published on: February 2, 2002
|
Bibliography
-
G. Brightwell, O. Häggström, and P. Winkler (1999),
Nonmonotonic behavior in hard-core and Widom--Rowlinson models,
J. Statist. Phys. 94, 415-435.
Math.
Review 2000c:82016
-
H.-O. Georgii, O. Häggström, and C. Maes (2001),
The random geometry of equilibrium phases, Phase Transitions and Critical
Phenomena, Volume 18 (C. Domb and J.L. Lebowitz, eds), pp 1-142,
Academic Press, London.
-
G.R. Grimmett (1999), Percolation (2nd edition), Springer,
New York.
Math.
Review 2001a:60114
-
O. Häggström (2000), Markov random fields and
percolation on general graphs, Adv. Appl. Probab. 32, 39-66.
Math.
Review 2001g:60246
-
F.P. Kelly (1985), Stochastic models of computer communication
systems J. Roy. Statist. Soc. B 47, 379-395.
Math.
Review 87m:60212a
-
J.C. Wheeler and B. Widom (1970) Phase equilibrium and critical
behavior in a two-component Bethe-lattice gas or three-component
Bethe-lattice solution, J. Chem. Phys. 52, 5334-5343.
|
|
|
|
|
|
|
|
| | | | |
Electronic Communications in Probability. ISSN: 1083-589X |
|
Context