Is the fuzzy Potts model gibbsian?
Annales de l'I.H.P. Probabilités et statistiques (2003)
- Volume: 39, Issue: 5, page 891-917
- ISSN: 0246-0203
Access Full Article
topHow to cite
topHäggström, Olle. "Is the fuzzy Potts model gibbsian?." Annales de l'I.H.P. Probabilités et statistiques 39.5 (2003): 891-917. <http://eudml.org/doc/77785>.
@article{Häggström2003,
author = {Häggström, Olle},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {fuzzy Potts model; Gibbs measure; quasilocality; random-cluster representation},
language = {eng},
number = {5},
pages = {891-917},
publisher = {Elsevier},
title = {Is the fuzzy Potts model gibbsian?},
url = {http://eudml.org/doc/77785},
volume = {39},
year = {2003},
}
TY - JOUR
AU - Häggström, Olle
TI - Is the fuzzy Potts model gibbsian?
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2003
PB - Elsevier
VL - 39
IS - 5
SP - 891
EP - 917
LA - eng
KW - fuzzy Potts model; Gibbs measure; quasilocality; random-cluster representation
UR - http://eudml.org/doc/77785
ER -
References
top- [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. Zbl1084.82514
- [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. Zbl0642.60102MR901151
- [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 Fields90 (1991) 111-148. Zbl0727.60118MR1124831
- [4] J. van den Berg, C. Maes, Disagreement percolation in the study of Markov fields, Ann. Probab.22 (1994) 749-763. Zbl0814.60096MR1288130
- [5] L. Chayes, Percolation and ferromagnetism on Z2: the q-state Potts cases, Stochastic Process. Appl.65 (1996) 209-216. Zbl0889.60096MR1425356
- [6] A.C.D. van Enter, On the possible failure of the Gibbs property for measures on lattice systems, Markov Proc. Related Fields2 (1996) 209-224. Zbl0878.60064MR1418413
- [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. Zbl1081.82558MR1330368
- [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. Zbl1101.82314MR1241537
- [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. Zbl0960.60099MR1766342
- [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. Zbl0960.60099
- [11] R. Fernández, C.-E. Pfister, Global specifications and nonquasilocality of projections of Gibbs measures, Ann. Probab.25 (1997) 1284-1315. Zbl0895.60096MR1457620
- [12] C.M. Fortuin, P.W. Kasteleyn, On the random-cluster model. I. Introduction and relation to other models, Physica57 (1972) 536-564. MR359655
- [13] H.-O. Georgii, Gibbs Measures and Phase Transitions, de Gruyter, New York, 1988. Zbl0657.60122MR956646
- [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. MR2014387
- [15] G.R. Grimmett, The stochastic random-cluster process, and the uniqueness of random-cluster measures, Ann. Probab.23 (1995) 1461-1510. Zbl0852.60105MR1379156
- [16] G.R. Grimmett, Percolation, Springer, New York, 1999. Zbl0926.60004
- [17] O. Häggström, Random-cluster representations in the study of phase transitions, Markov Proc. Related Fields4 (1998) 275-321. Zbl0922.60088MR1670023
- [18] O. Häggström, Positive correlations in the fuzzy Potts model, Ann. Appl. Probab.9 (1999) 1149-1159. Zbl0957.60099MR1728557
- [19] O. Häggström, Coloring percolation clusters at random, Stochastic Process. Appl.96 (2001) 213-242. Zbl1058.60090MR1865356
- [20] O. Häggström, J. Jonasson, R. Lyons, Coupling and Bernoullicity in random-cluster and Potts models, Bernoulli8 (2002) 275-294. Zbl1012.60086MR1913108
- [21] C. Külske, (Non-)Gibbsianness and phase transitions in random lattic spin models, Markov Proc. Related Fields5 (1999) 357-383. Zbl0953.60097MR1734240
- [22] C. Külske, Weakly Gibbsian representations for joint measures of quenched lattice spin models, Probab. Theory Related Fields119 (2001) 1-30. Zbl1052.82016MR1813038
- [23] H. Künsch, S. Geman, A. Kehagias, Hidden Markov random fields, Ann. Appl. Probab.5 (1995) 577-602. Zbl0842.60046MR1359820
- [24] L. Laanait, A. Messager, J. Ruiz, Phase coexistence and surface tensions for the Potts model, Comm. Math. Phys.105 (1986) 527-545. MR852089
- [25] C. Maes, K. Vande Velde, The fuzzy Potts model, J. Phys. A28 (1995) 4261-4271. Zbl0868.60081MR1351929
- [26] C.M. Newman, L.S. Schulman, Infinite clusters in percolation models, J. Stat. Phys.26 (1981) 26-628. Zbl0509.60095MR648202
- [27] A. Pisztora, Surface order large deviations for Ising, Potts and percolation models, Probab. Theory Related Fields104 (1996) 427-466. Zbl0842.60022MR1384040
- [28] R.H. Swendsen, J.-S. Wang, Nonuniversal critical dynamics in Monte Carlo simulations, Phys. Rev. Lett.58 (1987) 86-88.
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.