Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)



Conformal invariance in two-dimensional percolation

Authors: Robert Langlands, Philippe Pouliot and Yvan Saint-Aubin
Journal: Bull. Amer. Math. Soc. 30 (1994), 1-61
MSC (2000): Primary 82B43; Secondary 81-03, 81T40, 82B20, 82B27
MathSciNet review: 1230963
Full-text PDF

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [AB] M. Aizenman and David J. Barsky, Sharpness of the phase transition in percolation models, Comm. Math. Phys. 108 (1987), 489-526. MR 874906 (88c:82026)
  • [BH] S. R. Broadbent, J. H. Hammersley, Percolation processes, I. Crystals and mazes, Math. Proc. Cambridge Philos. Soc. 53 (1957), 629-641. MR 0091567 (19:989e)
  • [BPZ] A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov, Infinite conformal symmetry in two-dimensional quantum field theory, Nuclear Phys. B 241 (1984), 333-380. MR 757857 (86m:81097)
  • [C1] John L. Cardy, Conformal invariance and surface critical behavior, Nuclear Phys. B 240 (1984), 514-522.
  • [C2] -, Effect of boundary conditions on the operator content of two-dimensional conformally invariant theories, Nuclear Phys. B 275 (1986), 200-218. MR 858661 (87m:82066)
  • [C3] -, Boundary conditions, fusion rules and the Verlinde formula, Nuclear Phys. B 324 (1989), 581-596. MR 1019724 (91d:81118)
  • [C4] -, Critical percolation in finite geometries, J. Phys. A 25 (1992), L201. MR 1151081 (92m:82048)
  • [E1] John W. Essam, Graph theory and statistical physics, Discrete Math 1 (1971), 83-112. MR 0297279 (45:6336)
  • [E2] -, Percolation theory, Rep. Progr. Phys. 43 (1980), 833-912. MR 588142 (84m:82069)
  • [F1] M. E. Fisher, The theory of equilibrium critical phenomena, Rep. Progr. Phys. 30 (1967), 615-730.
  • [F2] -, Scaling, universality and renormalization group theory, Critical Phenomena (F. J. W. Hahne, ed.), Lecture Notes in Phys., vol. 186, Springer-Verlag, New York, 1983, pp. 1-139. MR 719887 (85b:82002)
  • [GJ] James Glimm and Arthur Jaffe, Quantum physics, Springer-Verlag, New York, 1981. MR 628000 (83c:81001)
  • [G] G. Grimmett, Percolation, Springer-Verlag, New York, 1989. MR 995460 (90j:60109)
  • [H] P. Heller, Experimental investigations of critical phenomena, Rep. Progr. Phys. 30 (1967), 731-826.
  • [K] H. Kesten, Percolation theory for mathematicians, Birkhäuser, Boston, 1982. MR 692943 (84i:60145)
  • [U] R. P. Langlands, C. Pichet, P. Pouliot, and Y. Saint-Aubin, On the universality of crossing probabilities in two-dimensional percolation, J. Statist. Phys. 67 (1992), 553-574. MR 1171144 (93e:82028)
  • [L] R. P. Langlands, Dualität bei endlichen Modellen der Perkolation, Math. Nach. 160 (1993), 7-58. MR 1244993 (95d:60161)
  • [LL] R. P. Langlands and M.-A. Lafortune, Finite models for percolation, submitted for publication in the Corwin Memorial Volume, Contemp. Math., Amer. Math. Soc., Providence, RI. MR 1303608 (95m:60163)
  • [M] David S. McLachlan, Michael Blaszkiewicz, and Robert E. Newnham, Electrical resistivity of composites, J. Amer. Ceram. Soc. 73 (1990), 2187-2203.
  • [NF] D. R. Nelson and M. E. Fisher, Soluble renormalization groups and scaling fields for the low-dimensional Ising systems, Ann. Physics 91 (1975), 226-274. MR 0391850 (52:12669)
  • [P] Jean Perrin, Les atomes, Coll. Idées, vol. 222, Gallimard, Paris, 1970.
  • [RW1] Alvany Rocha-Caridi and Nolan Wallach, Characters of irreducible representations of the Lie algebra of vector fields on the circle, Invent. Math. 72 (1983), 57-75. MR 696690 (85a:17010)
  • [RW2] -, Characters of irreducible representations of the Virasoro algebra, Math. Z. 185 (1984), 1-21. MR 724043 (85h:17008)
  • [SA] Yvan Saint-Aubin, Phénomènes critiques en deux dimensions et invariance conforme, Course notes, Univ. of Montréal, 1987.
  • [S] Jan V. Sengers and Anneke Levelt Sengers, The critical region, Chemical and Engineering News, 10 June 1968, pp. 104-118.
  • [Wo] Po-zen Wong, The statistical physics of sedimentary rock, Physics Today 41 (1988), 24-32.
  • [W] F. Y. Wu, The Potts model, Rev. Modern Phys. 54 (1982), 235-268. MR 641370 (84d:82033)
  • [Y] F. Yonezawa, S. Sakamoto, K. Aoki, S. Nosé, and M. Hori, Percolation in Penrose tiling and its dual--in comparison with analysis for Kagomé, dice and square lattices, J. Non-Crys. Solids 106 (1988), 262-269.
  • [Z] Robert Ziff, On the spanning probability in 2D percolation, Phys. Rev. Lett. 69 (1992), 2670-2673.

Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (2000): 82B43, 81-03, 81T40, 82B20, 82B27

Retrieve articles in all journals with MSC (2000): 82B43, 81-03, 81T40, 82B20, 82B27

Additional Information

Keywords: Percolation, conformal invariance, critical phenomena, conformal quantum field theory
Article copyright: © Copyright 1994 American Mathematical Society

American Mathematical Society