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We provide a new proof of the sharpness of the phase transition for Bernoulli percolation and the Ising model.
Crystal statistics. I. A two-dimensional model with an order-disorder transition
L. Onsager · 1944
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Percolation processes: Lower bounds for the critical probability
J. M. Hammersley · 1957
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A lower bound for the critical probability in a certain percolation process
T. E. Harris · 1960
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Correlation in Ising ferromagnets I, II
R. B. Griffiths · 1967
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Concavity of magnetization of an Ising ferromagnet in a positive external field
Robert B. Griffiths, C. A. Hurst, and S. Sherman · 1970
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A note on percolation
L. Russo · 1978
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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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A refinement of Simon’s correlation inequality
E. H. Lieb · 1980
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Correlation inequalities and the decay of correlations in ferromagnets
B. Simon · 1980
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Geometric analysis of φ 4 \varphi^{4} fields and Ising models. I, II
M. Aizenman · 1982
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Tree graph inequalities and critical behavior in percolation models
M. Aizenman and C. M. Newman · 1984
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On the critical behavior of the magnetization in high-dimensional Ising models
M. Aizenman and R. Fernández · 1986
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Coincidence of critical points in percolation problems
M. V. Menshikov · 1986
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Sharpness of the phase transition in percolation models
M. Aizenman and D. J. Barsky · 1987
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The phase transition
M. Aizenman, D. J. Barsky, and R. Fernández · 1987
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A short proof of the Harris-Kesten theorem
Béla Bollobás and Oliver Riordan · 2006
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The random-cluster model
G. Grimmett · 2006
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Sharpness of the phase transition and exponential decay of the subcritical cluster size for percolation on quasi-transitive graphs
T. Antunović and I. Veselić · 2008
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Is the critical percolation
I. Benjamini, A. Nachmias, and Y. Peres · 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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Smirnov’s fermionic observable away from criticality
V. Beffara and H. Duminil-Copin · 2012
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The mean field bound for the order parameter of Bernoulli percolation
J. T. Chayes and L. Chayes · 1987
Cited alongside, same era.
Percolation
G. Grimmett · 1999
Cited alongside, same era.
H. Duminil-Copin, V. Sidoravicius, and V. Tassion · 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
Closest in time.