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Phase transitions are a central theme of statistical mechanics, and of probability more generally.
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S. Miracle-Sol A. Messager · 1977
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Percolation probabilities on the square lattice
P. D. Seymour and D. J. A. Welsh · 1977
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Probabilistic computations: Toward a unified measure of complexity
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A note on percolation
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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}
H. Kesten · 1980
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The Kosterlitz-Thouless transition in two-dimensional abelian spin systems and the Coulomb gas
Jürg Fröhlich and Thomas Spencer · 1981
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Geometric analysis of φ 4 \varphi^{4} fields and Ising models. I, II
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Exactly solved models in statistical mechanics
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On the triviality of λ \lambda ϕ \phi d4 theories and the approach to the critical point in d (-)> 4 dimensions
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First-order phase transitions in large entropy lattice models
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Exact Critical Point and Critical Exponents of O ( n ) \mathrm{O}(n) Models in Two Dimensions
Bernard Nienhuis · 1982
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Ising model correlation functions: difference equations and applications to gauge theory
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Coulomb gas description of 2D critical behaviour
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Sharpness of the phase transition in percolation models
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Uniqueness of the infinite cluster and continuity of connectivity functions for short and long range percolation
M. Aizenman, H. Kesten, and C. M. Newman · 1987
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Bulk, surface, and interface properties of the Ising model and conformal invariance
Theodore W. Burkhardt and Ihnsouk Guim · 1987
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Discontinuity of the magnetization in one-dimensional 1 / | x − y | 2 1/|x-y|^{2} Ising and Potts models
M. Aizenman, J. T. Chayes, L. Chayes, and C. M. Newman · 1988
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Critical exponents for long-range interactions
M. Aizenman and Roberto Fernández · 1988
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The influence of variables on boolean functions
J. Kahn, G. Kalai, and N. Linial · 1988
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Density and uniqueness in percolation
R. M. Burton and M. Keane · 1989
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Mean-field critical behaviour for percolation in high dimensions
Takashi Hara and Gordon Slade · 1990
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Percolation in half-spaces: equality of critical densities and continuity of the percolation probability
D. J. Barsky, G. R. Grimmett, and Charles M. Newman · 1991
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Quantum group symmetries and nonlocal currents in 2 2 D QFT
Denis Bernard and André LeClair · 1991
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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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On Russo’s approximate zero-one law
M. Talagrand · 1994
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The connective constant of the honeycomb lattice equals 2 + 2 \sqrt{2+\sqrt{2}}
H. Duminil-Copin and S. Smirnov · 2012
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Random curves, scaling limits and loewner evolutions
Antti Kemppainen and Stanislav Smirnov · 2012
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Solving the 3d Ising model with the conformal bootstrap
El-Showk S., Paulos M. F., Poland D., Rychkov S., Simmons-Duffin D., and Vichi A · 2012
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Lectures on planar percolation with a glimpse of Schramm Loewner Evolution
V. Beffara and H. Duminil-Copin · 2013
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The critical temperature for the Ising model on planar doubly periodic graphs
D. Cimasoni and H. Duminil-Copin · 2013
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Critical percolation on any nonamenable group has no infinite clusters
I. Benjamini, Russell Lyons, Y. Peres, and Oded Schramm · 1999
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Percolation
G. Grimmett · 1999
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Inequalities and entanglements for percolation and random-cluster models
G. R. Grimmett · 1999
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Scaling limits of loop-erased random walks and uniform spanning trees
Oded Schramm · 2000
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Critical percolation in the plane: conformal invariance, Cardy’s formula, scaling limits
Stanislav Smirnov · 2001
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2D models of statistical physics with continuous symmetry: the case of singular interactions
D. Ioffe, S. Shlosman, and Y. Velenik · 2002
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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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The energy density in the planar Ising model
Clément Hongler and Stanislav Smirnov · 2013
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Discrete holomorphicity and quantized affine algebras
Y. Ikhlef, R. Weston, M. Wheeler, and P. Zinn-Justin · 2013
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The fermionic observable in the ising model and the inverse kac-ward operator
M. Lis · 2013
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The critical fugacity for surface adsorption of self-avoiding walks on the honeycomb lattice is 1 + 2 1+\sqrt{2}
N. R. Beaton, M. Bousquet-Mélou, J. de Gier, H. Duminil-Copin, and A. J. Guttmann · 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 model
H. Duminil-Copin, C. Garban, and G. Pete · 2014
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Planarité et localité en percolation
Vincent Tassion · 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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RSW and Box-Crossing Property for Planar Percolation
H. Duminil-Copin and V. Tassion · 2015
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Connective constant for a weighted self-avoiding walk on ℤ 2 \mathbb{Z}^{2}
A. Glazman · 2015
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Smirnov’s observable for free boundary conditions, interfaces and crossing probabilities
K. Izyurov · 2015
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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 · 2016
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Crossing probabilities in topological rectangles for the critical planar FK-Ising model
D. Chelkak, H. Duminil-Copin, and C. Hongler · 2016
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A proof of first order phase transition for the planar random-cluster and potts models with q ≫ 1 q\gg 1
H. Duminil-Copin · 2016
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Random currents expansion of the Ising model
H. Duminil-Copin · 2016
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The Bethe ansatz for the six-vertex and XXZ models: an exposition
H. Duminil-Copin, M. Gagnebin, M. Harel, I. Manolescu, and V. Tassion · 2016
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H. Duminil-Copin, M. Gagnebin, M. Harel, I. Manolescu, and V. Tassion · 2016
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The phase transitions of the planar random-cluster and Potts models with q ≥ 1 q\geq 1 are sharp
H. Duminil-Copin and I. Manolescu · 2016
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A new computation of the critical point for the planar random-cluster model with q ≥ 1 q\geq 1
H. Duminil-Copin, A. Raoufi, and V. Tassion · 2016
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Absence of infinite cluster for critical Bernoulli percolation on slabs
H. Duminil-Copin, V. Sidoravicius, and V. Tassion · 2016
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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 · 2016
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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 · 2016
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Critical percolation on any quasi-transitive graph of exponential growth has no infinite clusters
Tom Hutchcroft · 2016
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Marcin lis marcin lis [pdf] à partir de researchgate.net a short proof of the kac-ward formula
M. Lis · 2016
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Crossing probabilities for voronoi percolation
Vincent Tassion · 2016
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Exponential decay of loop lengths in the loop O ( n ) O(n) model with large n n
H. Duminil-Copin, R. Peled, W. Samotij, and Y. Spinka · 2017
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H. Duminil-Copin, A. Raoufi, and V. Tassion · 2017
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Sharp phase transition for the random-cluster and potts models via decision trees
H. Duminil-Copin, A. Raoufi, and V. Tassion · 2017
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Subcritical phase of d d -dimensional Poisson-boolean percolation and its vacant set
H. Duminil-Copin, A. Raoufi, and V. Tassion · 2017
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Continuity of the phase transition for planar random-cluster and Potts models with 1 ≤ q ≤ 4 1\leq q\leq 4
H. Duminil-Copin, V. Sidoravicius, and V. Tassion · 2017
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