Percolation and number of phases in the two-dimensional Ising model

Journal of Mathematical Physics

Volumn 41, Issue 3, 2000, Pages 1153-1169

  Georgii, Hans Otto ^a   Higuchi, Yasunari ^b  

^a UNIVERSITY OF MUNICH   (Germany)

^b KOBE UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034147077     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.533182     Document Type: Article

References (11)

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2. Y. Higuchi, "On the absence of non-transiation invariant Gibbs states for the two-dimensional Ising model," in Random Fields, Esztergom (Hungary), edited by J. Fritz, J. L. Lebowitz, and D. Szász (North-Holland, Amsterdam, 1979), Vol. 1. pp. 517-534.
3. L. Russo, "The infinite cluster method in the two-dimensional Ising model,Commun. Math. Phys. 67, 251-266 (1979).
4. A. Messager and S. Miracle-Solé, Equilibrium states of the two-dimensional Ising model in the two-phase region,Commun. Math. Phys. 40, 187-196 (1975).
5. R. Burton and M. Keane, Density and uniqueness in percolation,Commun. Math. Phys. 121, 501-505 (1989).
6. H.-O. Georgii, O. Häggströrn, and C. Maes, The random geometry of equilibrium phases,in Critical Phenomena, edited by C. Domb and J. L. Lebowitz (Academic, New York, 2000).
7. H-O. Georgii, Gibbs Measures and Phase Transitions (de Gruyter, Berlin, 1988).
8. A. Coniglio, C. R. Nappi, F. Peruggi, and L. Russo, "Percolation and phase transitions in the Ising model," Commun. Math. Phys. 51, 315-323 (1976).
9. A. Gandolfi, M. Keane, and L. Russo, "On the uniqueness of the infinite occupied cluster in dependent two-dimensional site percolation," Ann. Prob. 16, 1147-1157 (1988).
10. H. Fukuda, "The two-dimensional Ising model and Gibbs states, an approach with percolation method," Master thesis, Osaka University (in Japanese).
11. H. Kesten, Percolation Theory for Mathematicians (Birkhauser, Boston, 1982).