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This article studies the planar Potts model and its random-cluster representation.
Crystal statistics. I. A two-dimensional model with an order-disorder transition
Lars Onsager · 1944
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Some generalized order-disorder transformations
Renfrey Burnard Potts · 1952
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The spontaneous magnetization of a two-dimensional Ising model
C.N. Yang · 1952
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Generalized ferroelectric model on a square lattice
R. J. Baxter · 1971
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On the random-cluster model. I. Introduction and relation to other models
C. M. Fortuin and P. W. Kasteleyn · 1972
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Potts model at the critical temperature
R. J. Baxter · 1973
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Percolation probabilities on the square lattice
P. D. Seymour and D. J. A. Welsh · 1977
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A note on percolation
Lucio Russo · 1978
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Disorder variables and para-fermions in two-dimensional statistical mechanics
Eduardo Fradkin and Leo P Kadanoff · 1980
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The critical probability of bond percolation on the square lattice equals 1 2 {1\over 2}
Harry Kesten · 1980
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Correlation inequalities and the decay of correlations in ferromagnets
Barry Simon · 1980
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Exactly solved models in statistical mechanics
Rodney J. Baxter · 1982
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First-order phase transitions in large entropy
R. Kotecký and S. B. Shlosman · 1982
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The Potts model
F. Y. Wu · 1982
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Infinite conformal symmetry
A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov · 1984
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Infinite conformal symmetry of critical fluctuations in two dimensions
A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov · 1984
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On the critical behavior of the magnetization
M. Aizenman and R. Fernández · 1986
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Phases coexistence and surface tensions
L. Laanait, A. Messager, and J. Ruiz · 1986
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Interfaces in the Potts model. I. Pirogov-Sinai theory of the Fortuin-Kasteleyn representation
Lahoussine Laanait, Alain Messager, Salvador Miracle-Solé, Jean Ruiz, and Senya Shlosman · 1991
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On weak mixing in lattice models
Kenneth S. Alexander · 1998
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Hölder regularity and dimension bounds for random curves
M. Aizenman and A. Burchard · 1999
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Conformal invariance of domino tiling
Richard Kenyon · 2000
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Dominos and the Gaussian free field
Richard Kenyon · 2001
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Conformal invariance
Gregory F. Lawler, Oded Schramm, and Wendelin Werner · 2004
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Conformally invariant processes in the plane
Gregory F. Lawler · 2005
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Mean-field driven first-order phase transitions in systems with long-range interactions
Marek Biskup, Lincoln Chayes, and Nicholas Crawford · 2006
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The random-cluster model
Random curves, scaling limits and loewner evolutions
Antti Kemppainen and Stanislav Smirnov · 2012
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Critical Ising on the square lattice mixes in polynomial time
Eyal Lubetzky and Allan Sly · 2012
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On the critical parameters of the q ≥ 4 q\geq 4 random-cluster model on isoradial graphs
V. Beffara, H. Duminil-Copin, and S. Smirnov · 2013
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D. Chelkak, H. Duminil-Copin, and C. Hongler · 2013
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Holomorphic spinor observables in the critical Ising model
Dmitry Chelkak and Konstantin Izyurov · 2013
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Geoffrey Grimmett · 2006
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Holomorphic parafermions in the Potts model and stochastic Loewner evolution
V. Riva and J. Cardy · 2006
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Towards conformal invariance of 2D lattice models
Stanislav Smirnov · 2006
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Critical percolation exploration path and SLE 6 {\rm SLE}_{6} : a proof of convergence
F. Camia and C.M. Newman · 2007
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Conformally invariant scaling limits: an overview and a collection of problems
Oded Schramm · 2007
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Percolation et modèle d’Ising
Wendelin Werner · 2009
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H. Duminil-Copin · 2013
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Ising interfaces and free boundary conditions
Clément Hongler and Kalle Kytölä · 2013
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Conformal invariance of crossing probabilities for the Ising model with free boundary conditions
S. Benoist, H. Duminil-Copin, and C. Hongler · 2014
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Convergence of Ising interfaces to Schramm’s SLE curves
D. Chelkak, H. Duminil-Copin, C. Hongler, A. Kemppainen, and S. Smirnov · 2014
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The near-critical planar FK-Ising
H. Duminil-Copin, C. Garban, and G. Pete · 2014
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Bond percolation on isoradial graphs: criticality and universality
Geoffrey R. Grimmett and Ioan Manolescu · 2014
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Conformal invariance of Ising model correlations
C. Hongler · 2014
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Random Currents and Continuity of Ising Model’s Spontaneous Magnetization
M. Aizenman, H. Duminil-Copin, and V. Sidoravicius · 2015
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Conformal invariance of spin correlations in the planar Ising model
Dmitry Chelkak, Clément Hongler, and Konstantin Izyurov · 2015
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Geometric representations of lattice spin models
H. Duminil-Copin · 2015
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Universality for random-cluster models on isoradial graphs
H. Duminil-Copin, J.-H. Li, and I. Manolescu · 2015
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Random-cluster model with critical weights on isoradial graphs
H. Duminil-Copin and I. Manolescu · 2015
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A new proof of the sharpness of the phase transition for Bernoulli percolation and the Ising model
H. Duminil-Copin and V. Tassion · 2015
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A new proof of the sharpness of the phase transition for Bernoulli percolation on ℤ d \mathbb{Z}^{d}
H. Duminil-Copin and V. Tassion · 2015
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