@article{AIHPB_2001__37_6_643_0, author = {Cerf, Rapha\"el and Pisztora, \'Agoston}, title = {Phase coexistence in {Ising,} {Potts} and percolation models}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, pages = {643--724}, publisher = {Elsevier}, volume = {37}, number = {6}, year = {2001}, mrnumber = {1863274}, zbl = {1006.60094}, language = {en}, url = {http://archive.numdam.org/item/AIHPB_2001__37_6_643_0/} }
TY - JOUR AU - Cerf, Raphaël AU - Pisztora, Ágoston TI - Phase coexistence in Ising, Potts and percolation models JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2001 SP - 643 EP - 724 VL - 37 IS - 6 PB - Elsevier UR - http://archive.numdam.org/item/AIHPB_2001__37_6_643_0/ LA - en ID - AIHPB_2001__37_6_643_0 ER -
%0 Journal Article %A Cerf, Raphaël %A Pisztora, Ágoston %T Phase coexistence in Ising, Potts and percolation models %J Annales de l'I.H.P. Probabilités et statistiques %D 2001 %P 643-724 %V 37 %N 6 %I Elsevier %U http://archive.numdam.org/item/AIHPB_2001__37_6_643_0/ %G en %F AIHPB_2001__37_6_643_0
Cerf, Raphaël; Pisztora, Ágoston. Phase coexistence in Ising, Potts and percolation models. Annales de l'I.H.P. Probabilités et statistiques, Tome 37 (2001) no. 6, pp. 643-724. http://archive.numdam.org/item/AIHPB_2001__37_6_643_0/
[1] Cube-root boundary fluctuations for droplets in random cluster models, Preprint, 2000. | MR
,[2] Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints, Mem. Amer. Math. Soc. 4 (165) (1976). | MR | Zbl
,[3] Surface tension in Ising systems with Kac potentials, J. Stat. Phys. 82 (1996) 743-796. | MR | Zbl
, , , ,[4] The Wulff construction and asymptotics of the finite cluster distribution for two-dimensional Bernoulli percolation, Comm. Math. Phys. 131 (1990) 1-50. | MR | Zbl
, , ,[5] Functionals defined on partitions in sets of finite perimeter I: Integral representation and Γ-convergence, J. Math. Pures et Appl. 69 (1990) 285-305. | Zbl
, ,[6] Functionals defined on partitions in sets of finite perimeter II: Semicontinuity, relaxation and homogenization, J. Math. Pures et Appl. 69 (1990) 307-333. | MR | Zbl
, ,[7] Some regularity results for minimal crystals, Preprint, 2000. | Numdam | MR
, , ,[8] Assouad P., Quentin de Gromard T., Sur la dérivation des mesures dans Rn, Note (1998).
[9] On the validity of van der Waals theory of surface tension, Markov Process. Rel. Fields 3 (1997) 175-198. | MR | Zbl
, , , ,[10] Large deviations in the van der Waals limit, Stochastic Process. Appl. 75 (1998) 89-104. | MR | Zbl
, , ,[11] A general form of the covering principle and relative differentiation of additive functions, Proc. Cambridge Philos. Soc. 41 (1945) 103-110, Part II. Proc. Cambridge Philos. Soc. 42 (1946) 1-10. | Zbl
,[12] The Wulff construction in three and more dimensions, Comm. Math. Phys. 207 (1) (1999) 197-229. | MR | Zbl
,[13] Rigorous probabilistic analysis of equilibrium crystal shapes, J. Math. Phys. 41 (3) (2000) 1033-1098. | MR | Zbl
, , ,[14] Large deviations for three dimensional supercritical percolation, Astérisque 267 (2000). | Numdam | MR | Zbl
,[15] On the Wulff crystal in the Ising model, Ann. Probab. 28 (3) (2000) 945-1015. | MR | Zbl
, ,[16] Optimal partitions with unbounded data, Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat., IX Ser., Rend. Lincei., Mat. Appl. 4 (2) (1993) 103-108. | MR | Zbl
, ,[17] On the existence of solutions to a problem in multidimensional segmentation, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 8 (2) (1991) 175-195. | Numdam | MR | Zbl
, ,[18] Regularity properties of optimal segmentations, J. Reine Angew. Math. 420 (1991) 61-84. | MR | Zbl
, ,[19] Nuovi teoremi relativi alle misure (r−1)-dimensionali in uno spazio ad r dimensioni, Ricerche Mat. 4 (1955) 95-113. | Zbl
,[20] Frontiere orientate di misura minima e questioni collegate, Scuola Normale Superiore di Pisa (1972). | MR | Zbl
, , ,[21] Surface order large deviations for high-density percolation, Probab. Theory Relat. Fields 104 (1996) 467-482. | MR | Zbl
, ,[22] Wulff Construction: A Global Shape from Local Interaction, AMS Translations Series, Providence, RI, 1992. | MR | Zbl
, , ,[23] Thermodynamic inequalities for the surface tension and the geometry of the Wulff construction, in: (Ed.), Ideas and Methods in Quantum and Statistical Physics, Cambridge University Press, 1992, pp. 461-483. | MR | Zbl
, ,[24] Measure Theory and Fine Properties of Functions, Studies in Advanced Mathematics, CRC Press, Boca Raton, 1992. | MR | Zbl
, ,[25] The Geometry of Fractal Sets, Cambridge Tracts in Mathematics, 85, Cambridge Univ. Press, 1985. | MR | Zbl
,[26] Geometric Measure Theory, Springer-Verlag, 1969. | MR | Zbl
,[27] On the random-cluster model. I. Introduction and relation to other models, Physica 57 (1972) 536-564. | MR
, ,[28] Minimal Surfaces and Functions of Bounded Variation, Birkhäuser, 1984. | MR | Zbl
,[29] Percolation, Grundlehren der Mathematischen Wissenschaften, 321, Springer-Verlag, Berlin, 1999. | MR | Zbl
,[30] The stochastic random-cluster process and the uniqueness of random-cluster measures, Ann. Probab. 23 (1995) 1461-1510. | MR | Zbl
,[31] The supercritical phase of percolation is well behaved, Proc. R. Soc. Lond. Ser. A 430 (1990) 439-457. | MR | Zbl
, ,[32] The double bubble conjecture, Electron. Res. Announc. Amer. Math. Soc. 1 (3) (1995) 98-102, (electronic). | MR | Zbl
, , ,[33] Large deviations for the 2D Ising model: a lower bound without cluster expansions, J. Stat. Phys. 74 (1993) 411-432. | MR | Zbl
,[34] Exact large deviation bounds up to Tc for the Ising model in two dimensions, Probab. Theory Relat. Fields 102 (1995) 313-330. | MR | Zbl
,[35] Dobrushin-Kotecký-Shlosman Theorem up to the critical temperature, Comm. Math. Phys. 199 (1998) 117-167. | MR | Zbl
, ,[36] The probability of a large finite cluster in supercritical Bernoulli percolation, Ann. Probab. 18 (1990) 537-555. | MR | Zbl
, ,[37] Differential Manifolds, Springer-Verlag, 1985. | MR | Zbl
,[38] Paired calibrations applied to soap films, immiscible fluids, and surfaces or networks minimizing other norms, Pacific J. Math. 166 (1) (1994) 55-82. | MR | Zbl
, ,[39] An Ising interface between two walls: competition between two tendencies, Rev. Math. Phys. 8 (5) (1996) 669-687. | MR | Zbl
, , ,[40] Optimal subdivisions of n-dimensional domains. Ph.D. Thesis, Università di Trento, 1998.
,[41] Minimal Surfaces of Codimension One, North-Holland Mathematics Studies 91, Notas de Matematica, 95, North-Holland, 1984. | MR | Zbl
, ,[42] Sull'approssimazione degli aperti lipschitziani di Rn con varietà differenziabili, Bollettino U.M.I. (4) 10 (1974) 532-544. | MR | Zbl
, ,[43] Convexity properties of the surface tension and equilibrium crystals, J. Stat. Phys. 67 (3/4) (1992) 449-469. | MR | Zbl
, , ,[44] Surface tension, step free energy, and facets in the equilibrium crystal, J. Stat. Phys. 79 (1/2) (1995) 183-214. | Zbl
,[45] Topics in Disordered Systems, Lectures in Mathematics, ETH Zürich, Birkhäuser, 1997. | MR | Zbl
,[46] Large deviations and phase separation in the two-dimensional Ising model, Helv. Phys. Acta 64 (1991) 953-1054. | MR
,[47] Interface, surface tension and reentrant pinning transition in the 2D Ising model, Comm. Math. Phys. 204 (2) (1999) 269-312. | MR | Zbl
, ,[48] Large deviations and continuum limit in the 2D Ising model, Probab. Theory Related Fields 109 (1997) 435-506. | MR | Zbl
, ,[49] Surface order large deviations for Ising, Potts and percolation models, Probab. Theory Related Fields 104 (1996) 427-466. | MR | Zbl
,[50] Approximation forte dans BV(Ω), C. R. Acad. Sci. Paris, Ser. I 301 (1985) 261-264. | Zbl
,[51] Second order large deviation estimates for ferromagnetic systems in the phase coexistence region, Comm. Math. Phys. 112 (1987) 409-422. | MR
,[52] Ph.D. Thesis, EPFL, 1997.
,[53] The spaces BV and quasilinear equations, Math. USSR Sb. 2 (1967) 225-267. | MR | Zbl
,[54] Weakly Differentiable Functions. Sobolev Spaces and Functions of Bounded Variation, Graduate Texts in Mathematics, 120, Springer-Verlag, 1989. | MR | Zbl
,