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

   
@article{ECP1048,
	author = {Olle Häggström},
	title = {A Monotonicity Result for Hard-core and Widom-Rowlinson Models on Certain $d$-dimensional Lattices},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {7},
	year = {2002},
	keywords = {Hard-core model, Widom-Rowlinson model, Gibbsmeasures, monotonic phase transition, site-random-cluster model.},
	abstract = {For each $d\geq 2$, 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.},
	pages = {no. 7, 67-78},
	issn = {1083-589X},
	doi = {10.1214/ECP.v7-1048},    
        url = {http://ecp.ejpecp.org/article/view/1048}}