Phase transition in the random triangle model

Journal of Applied Probability

Volumn 36, Issue 4, 1999, Pages 1101-1115

  Häggström, Olle ^a   Jonasson, Johan ^a  

^a CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

Ising model; Percolation; Planar duality; Stochastic domination

Indexed keywords

EID: 0033233838     PISSN: 00219002     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0021900200017897     Document Type: Article

References (23)

1. BAXTER, R. J. (1982). Exactly Solved Models in Statistical Mechanics. Academic Press, London.
2. BOLLOBÁS, B. (1985). Random Graphs. Academic Press, London.
3. BROADBENT, S. R. AND HAMMERSLEY, J. M. (1957). Percolation processes I. Crystals and mazes. Proc. Cambridge Phil. Soc. 53, 629-641.
4. BURTON, R. AND KEANE, M. (1989). Density and uniqueness in percolation. Commun. Math. Phys. 121, 501-505.
5. ELLIS, R. S. (1985). Entropy, Large Deviations and Statistical Mechanics. Springer, New York.
6. ERDOS, P. AND RÉNYI, A. (1959). On random graphs I. Publ. Math. Debrecen 6, 290-297.
7. FAUST, K. AND WASSERMAN, S. (1994). Social Network Analysis. CUP, Cambridge.
8. FORTUIN, C. M. AND KASTELEYN, P. W. (1972). On the random cluster model. I. Introduction and relation to other models. Physica 58, 393-418.
9. FRANK, O. (1988). Random sampling and social networks: A survey of various approaches. Math. Sci. Humaines 104, 19-33.
10. GANDOLFI, A., KEANE, M. AND RUSSO, L. (1988). On the uniqueness of the infinite occupied cluster in dependent two-dimensional site percolation. Ann. Prob. 16, 1147-1157.
11. GEORGII, H.-O. (1988). Gibbs Measures and Phase Transitions. De Gruyter, New York.
12. GRIMMETT, G. (1989). Percolation. Springer, New York.
13. GRIMMETT, G. (1995). The stochastic random-cluster process and the uniqueness of random-cluster measures. Ann. Prob. 23, 1461-1510.
14. 2 with parity-dependent activities. Ark. Mat. 35, 171-184.
15. HÄGGSTRÖM, O. (1998). Random-cluster representations in the study of phase transitions. Markov Proc. Rel. Fields 4, 275-321.
16. HOLLEY, R. (1974). Remarks on the FKG inequalities. Commun. Math. Phys. 36, 227-231.
17. JONASSON, J. (1997). The random triangle model. J. Appl. Prob. 36, 852-867.
18. JONASSON, J. AND STEIF, J. (1999). Amenability and phase transition in the Ising model. J. Theor. Prob. 12, 549-559.
19. KOTECKÝ, R. (1994). Geometric representation of lattice models and large volume asymptotics. In Probability and Phase Transition, ed. G. Grimmett. Kluwer, Dordrecht.
20. LIGGETT, T. (1985). Interacting Particle Systems. Springer, New York.
21. LINDVALL, T. (1992). Lectures on the Coupling Method. Wiley, New York.
22. SPITZER, F. (1975). Markov random fields on an infinite tree. Ann. Prob. 3, 387-398.
23. WIERMAN, J. C. (1981). Bond percolation on honeycomb and triangular lattices. Adv. Appl. Prob. 13, 298-313.