no. 5
Is the fuzzy Potts model gibbsian?
Annales de l'I.H.P. Probabilités et statistiques, Tome 39 (2003) no. 5, pp. 891-917. 
@article{AIHPB_2003__39_5_891_0,
     author = {H\"aggstr\"om, Olle},
     title = {Is the fuzzy {Potts} model gibbsian?},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {891--917},
     publisher = {Elsevier},
     volume = {39},
     number = {5},
     year = {2003},
     doi = {10.1016/S0246-0203(03)00026-8},
     mrnumber = {1997217},
     zbl = {1033.60094},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/S0246-0203(03)00026-8/}
}
TY  - JOUR
AU  - Häggström, Olle
TI  - Is the fuzzy Potts model gibbsian?
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 2003
SP  - 891
EP  - 917
VL  - 39
IS  - 5
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/S0246-0203(03)00026-8/
DO  - 10.1016/S0246-0203(03)00026-8
LA  - en
ID  - AIHPB_2003__39_5_891_0
ER  - 
%0 Journal Article
%A Häggström, Olle
%T Is the fuzzy Potts model gibbsian?
%J Annales de l'I.H.P. Probabilités et statistiques
%D 2003
%P 891-917
%V 39
%N 5
%I Elsevier
%U http://www.numdam.org/articles/10.1016/S0246-0203(03)00026-8/
%R 10.1016/S0246-0203(03)00026-8
%G en
%F AIHPB_2003__39_5_891_0
Häggström, Olle. Is the fuzzy Potts model gibbsian?. Annales de l'I.H.P. Probabilités et statistiques, Tome 39 (2003) no. 5, pp. 891-917. doi : 10.1016/S0246-0203(03)00026-8. http://www.numdam.org/articles/10.1016/S0246-0203(03)00026-8/

[1] M. Aizenman, J.T. Chayes, L. Chayes, C.M. Newman, Discontinuity of the magnetization in one-dimensional 1/|x−y|2 Ising and Potts models, J. Stat. Phys. 50 (1988) 1-40. | Zbl

[2] M. Aizenman, H. Kesten, C.M. Newman, Uniqueness of the infinite cluster and continuity of connectivity functions for short- and long-range percolation, Comm. Math. Phys. 111 (1987) 505-532. | MR | Zbl

[3] D.J. Barsky, G.R. Grimmett, C.M. Newman, Percolation in half-spaces: equality of critical densities and continuity of the percolation probability, Probab. Theory Related Fields 90 (1991) 111-148. | MR | Zbl

[4] J. Van Den Berg, C. Maes, Disagreement percolation in the study of Markov fields, Ann. Probab. 22 (1994) 749-763. | MR | Zbl

[5] L. Chayes, Percolation and ferromagnetism on Z2: the q-state Potts cases, Stochastic Process. Appl. 65 (1996) 209-216. | MR | Zbl

[6] A.C.D. Van Enter, On the possible failure of the Gibbs property for measures on lattice systems, Markov Proc. Related Fields 2 (1996) 209-224. | MR | Zbl

[7] A.C.D. Van Enter, R. Fernández, R. Kotecký, Pathological behavior of renormalization-group maps at high fields and above the transition temperature, J. Stat. Phys. 79 (1995) 969-992. | MR | Zbl

[8] A.C.D. Van Enter, R. Fernández, A.D. Sokal, Regularity properties of position-space renormalization group transformations: Scope and limitations of Gibbsian theory, J. Stat. Phys. 72 (1993) 879-1167. | MR | Zbl

[9] A.C.D. Van Enter, C. Maes, R.H. Schonmann, S. Shlosman, The Griffiths singularity random field, in: Minlos R., Suhov Yu., Shlosman S. (Eds.), On Dobrushin's Way. From Probability to Statistical Mechanics, American Mathematical Society, 2000, pp. 59-70. | MR | Zbl

[10] A.C.D. Van Enter, C. Maes, S. Shlosman, Dobrushin's program on Gibbsianity restoration: weakly Gibbs and almost Gibbs random fields, in: Minlos R., Suhov Yu., Shlosman S. (Eds.), On Dobrushin's Way. From Probability to Statistical Mechanics, American Mathematical Society, 2000, pp. 51-58. | Zbl

[11] R. Fernández, C.-E. Pfister, Global specifications and nonquasilocality of projections of Gibbs measures, Ann. Probab. 25 (1997) 1284-1315. | MR | Zbl

[12] C.M. Fortuin, P.W. Kasteleyn, On the random-cluster model. I. Introduction and relation to other models, Physica 57 (1972) 536-564. | MR

[13] H.-O. Georgii, Gibbs Measures and Phase Transitions, de Gruyter, New York, 1988. | MR | Zbl

[14] H.-O. Georgii, O. Häggström, C. Maes, The random geometry of equilibrium phases, in: Domb C., Lebowitz J.L. (Eds.), Phase Transitions and Critical Phenomena, Vol. 18, Academic Press, London, 2001, pp. 1-142. | MR

[15] G.R. Grimmett, The stochastic random-cluster process, and the uniqueness of random-cluster measures, Ann. Probab. 23 (1995) 1461-1510. | MR | Zbl

[16] G.R. Grimmett, Percolation, Springer, New York, 1999. | Zbl

[17] O. Häggström, Random-cluster representations in the study of phase transitions, Markov Proc. Related Fields 4 (1998) 275-321. | MR | Zbl

[18] O. Häggström, Positive correlations in the fuzzy Potts model, Ann. Appl. Probab. 9 (1999) 1149-1159. | MR | Zbl

[19] O. Häggström, Coloring percolation clusters at random, Stochastic Process. Appl. 96 (2001) 213-242. | MR | Zbl

[20] O. Häggström, J. Jonasson, R. Lyons, Coupling and Bernoullicity in random-cluster and Potts models, Bernoulli 8 (2002) 275-294. | MR | Zbl

[21] C. Külske, (Non-)Gibbsianness and phase transitions in random lattic spin models, Markov Proc. Related Fields 5 (1999) 357-383. | MR | Zbl

[22] C. Külske, Weakly Gibbsian representations for joint measures of quenched lattice spin models, Probab. Theory Related Fields 119 (2001) 1-30. | MR | Zbl

[23] H. Künsch, S. Geman, A. Kehagias, Hidden Markov random fields, Ann. Appl. Probab. 5 (1995) 577-602. | MR | Zbl

[24] L. Laanait, A. Messager, J. Ruiz, Phase coexistence and surface tensions for the Potts model, Comm. Math. Phys. 105 (1986) 527-545. | MR

[25] C. Maes, K. Vande Velde, The fuzzy Potts model, J. Phys. A 28 (1995) 4261-4271. | MR | Zbl

[26] C.M. Newman, L.S. Schulman, Infinite clusters in percolation models, J. Stat. Phys. 26 (1981) 26-628. | MR | Zbl

[27] A. Pisztora, Surface order large deviations for Ising, Potts and percolation models, Probab. Theory Related Fields 104 (1996) 427-466. | MR | Zbl

[28] R.H. Swendsen, J.-S. Wang, Nonuniversal critical dynamics in Monte Carlo simulations, Phys. Rev. Lett. 58 (1987) 86-88.

Cité par Sources :