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We present a new computation of the critical value of the random-cluster model with cluster weight $q\ge 1$ on $\mathbb{Z}^2$.
On the random-cluster model. I. Introduction and relation to other models
C. M. Fortuin and P. W. Kasteleyn · 1972
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On the critical percolation probabilities
L. Russo · 1981
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The influence of variables in product spaces
Jean Bourgain, Jeff Kahn, Gil Kalai, Yitzhak Katznelson, and Nathan Linial · 1992
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Greedy lattice animals. II. Linear growth
Alberto Gandolfi and H. Kesten · 1994
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Decay of correlations in random-cluster models
G. R. Grimmett and M.S.T. Piza · 1997
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The critical probability for random Voronoi percolation in the plane is 1/2
Béla Bollobás and Oliver Riordan · 2006
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A short proof of the Harris-Kesten theorem
Béla Bollobás and Oliver Riordan · 2006
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Influence and sharp-threshold theorems for monotonic measures
B. T. Graham and G. R. Grimmett · 2006
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The random-cluster model
G. Grimmett · 2006
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Sharp thresholds for the random-cluster and Ising models
Benjamin Graham and G. Grimmett · 2011
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The self-dual point of the two-dimensional random-cluster model is critical for q ≥ 1 q\geq 1
V. Beffara and H. Duminil-Copin · 2012
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Parafermionic observables and their applications to planar statistical physics models
H. Duminil-Copin · 2013
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The phase transitions of the planar random-cluster and potts models with q larger than 1 are sharp
Hugo Duminil-Copin and Ioan Manolescu · 2014
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Crossing probabilities for voronoi percolation
Vincent Tassion · 2014
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Absence of infinite cluster for critical bernoulli percolation on slabs
H. Duminil-Copin, V. Sidoravicius, and V. Tassion · 2015
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