Crossing probabilities in topological rectangles for the critical planar FK-Ising model

W. Lenz, Beitrag zum verständnis der magnetischen eigenschaften in festen körpern. , Phys. Zeitschr. 21

1920

Earlier work this paper cites.

E. Ising, Beitrag zur theorie des ferromagnetismus. , Z. Phys. 31

1925

Earlier work this paper cites.

R. Peierls, On Ising’s model of ferromagnetism. , Math. Proc. Camb. Phil. Soc. 32

1936

Earlier work this paper cites.

L. Onsager, Crystal statistics. I. A two-dimensional model with an order-disorder transition. , Phys. Rev. (2) 65

1944

Earlier work this paper cites.

C. M. Fortuin and P. W. Kasteleyn, On the random-cluster model. I. Introduction and relation to other models , Physica 57

1972

Earlier work this paper cites.

P. D. Seymour and D. J. A. Welsh, Percolation probabilities on the square lattice , Ann. Discrete Math. 3

1977

Earlier work this paper cites.

L. Russo, A note on percolation , Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 43

1978

Earlier work this paper cites.

H. Kesten, Scaling relations for 2 2 D-percolation , Comm. Math. Phys. 109

1987

Earlier work this paper cites.

R. Langlands, P. Pouliot, and Y. Saint-Aubin, Conformal invariance in two-dimensional percolation , Bull. Amer. Math. Soc. (N.S.) 30

1994

Earlier work this paper cites.

M. Aizenman and A. Burchard, Hölder regularity and dimension bounds for random curves , Duke Math. J. 99

1999

Earlier work this paper cites.

M. Bauer, D. Bernard, and K. Kytölä, Multiple Schramm-Loewner evolutions and statistical mechanics martingales , J. Stat. Phys. 120

2005

Earlier work this paper cites.

M. Niss, History of the Lenz-Ising model 1920–1950: from ferromagnetic to cooperative phenomena , Archive for history of exact sciences 59

2005

Cited alongside, same era.

F. Camia and C. M. Newman, Two-dimensional critical percolation: the full scaling limit , Comm. Math. Phys. 268

2006

Cited alongside, same era.

G. Grimmett, The random-cluster model , Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 333, Springer-Verlag, Berlin, 2006

2006

Cited alongside, same era.

S. Smirnov, Towards conformal invariance of 2D lattice models , International Congress of Mathematicians. Vol. II, Eur. Math. Soc., Zürich, 2006, pp. 1421–1451

2006

Cited alongside, same era.

P. Nolin, Near-critical percolation in two dimensions , Electron. J. Probab. 13

2008

Cited alongside, same era.

V. Beffara and H. Duminil-Copin, The self-dual point of the two-dimensional random-cluster model is critical for q ⩾ 1 q\geqslant 1 , Probab. Theory Related Fields 153

2012

Later among the works it cites.

F. Camia, C. Garban, and C. M. Newman, Planar Ising magnetization field I. Uniqueness of the critical scaling limit , Arxiv preprint arXiv:1205.6610 [math.PR] (2012)

Original

2012

Later among the works it cites.

D. Chelkak, Robust discrete complex analysis: a toolbox , Arxiv preprint arXiv:1212.6205 [math.PR] (2012), to appear in Ann. Probab

Original

2012

Later among the works it cites.

D. Chelkak and S. Smirnov, Universality in the 2D Ising model and conformal invariance of fermionic observables , Invent. Math. 189

2012

Later among the works it cites.

H. Duminil-Copin, C. Garban, and G. Pete, The near-critical planar FK-Ising model , Arxiv preprint arXiv:1111.0144 [math.PR] (2012), to appear in Comm. Math. Phys