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We prove that the scaling limits of spin fluctuations in four-dimensional Ising-type models with nearest-neighbor ferromagnetic interaction at or near the critical point are Gaussian.
M.G. Krein, M.A. Rutman, Linear operators leaving invariant a cone in a Banach space , Transl. Amer. Math. Soc.26, 199 (1950) (cf. p.279)
1950
Earlier work this paper cites.
A.S. Wightman, Quantum Field Theory in Terms of Vacuum Expectation Values , Phys. Rev. 101, 860, 1956
1956
Earlier work this paper cites.
Percolation processes: Lower bounds for the critical probability
J.M. Hammersley · 1957
Earlier work this paper cites.
T.D. Schultz, D.C. Mattis, E.H. Lieb, Two-dimensional Ising model as a soluble problem of many fermions , Reviews of Modern Physics 36(3), 856, 1964
1964
Earlier work this paper cites.
R. Griffiths, Correlation in Ising ferromagnets I, II
1967
Earlier work this paper cites.
R. Griffiths, Rigorous Results for Ising Ferromagnets of Arbitrary Spin
1969
Earlier work this paper cites.
K. Symanzik, Euclidean quantum field theory , Local quantum theory. Jost, R. (ed.). New York: Academic Press, 1969
1969
Earlier work this paper cites.
R.B. Griffiths, C.A. Hurst, and S. Sherman, Concavity of magnetization of an Ising ferromagnet in a positive external field , J. Math. Phys., 11:790–795, 1970
1970
Earlier work this paper cites.
K.G. Wilson, Renormalization Group and Critical Phenomena. I. Renormalization Group and the Kadanoff Scaling Picture , Phys. Rev. B
1971
Earlier work this paper cites.
J. Glimm and A. Jaffe, Positivity of the ϕ 3 4 \phi_{3}^{4} hamiltonian. , Fortschritte der Physik, 21(7):327–376, 1973
1973
Earlier work this paper cites.
K. Osterwalder, R. Schrader, Axioms for Euclidean Green’s functions I. , Comm. Math. Phys. 31:83–112, 1973
1973
Earlier work this paper cites.
B. Simon and R.B. Griffiths, The ϕ 2 4 \phi^{4}_{2} field theory as a classical Ising model , Comm. Math. Phys. 33(2):145–164, 1973
1973
Earlier work this paper cites.
J.L. Lebowitz, GHS and other inequalities , Comm. Math. Phys. 35:87–92, 1974
1974
Earlier work this paper cites.
B. Simon, The P ( Φ ) 2 P(\Phi)_{2} Euclidean (Quantum) Field Theory, Princeton Univ. Press
1974
Earlier work this paper cites.
F. Guerra, L. Rosen and B. Simon, The P ( ϕ ) 2 P(\phi)^{2} Euclidean Quantum Field Theory as Classical Statistical Mechanics , Annals of Math., 101:111–189, 1975
1975
Earlier work this paper cites.
C.M. Newman, Inequalities for Ising models and field theories which obey the Lee-Yang theorem , Comm. Math. Phys., 41(1), 1975
1975
Earlier work this paper cites.
K. Osterwalder, R. Schrader, Axioms for Euclidean Green’s functions II. , Comm. Math. Phys. 42:281–305, 1975
1975
Earlier work this paper cites.
J. Fröhlich, B. Simon, and T. Spencer, Infrared bounds, phase transitions and continuous symmetry breaking , Comm. Math. Phys., 50(1):79–95, 1976
1976
Cited alongside, same era.
Correlation inequalities for Ising ferromagnets with symmetries
G.C. Hegerfeldt, · 1977
Cited alongside, same era.
S. Miracle-Solé A. Messager, Correlation functions and boundary conditions in the Ising ferromagnet , J. Stat. Phys. 17(4):245–262, 1977
1977
Cited alongside, same era.
R. Schrader. New correlation inequalities for the Ising model and P ( ϕ ) P(\phi) theories , Phys. Rev., B15:2798, 1977
1977
Cited alongside, same era.
J. Fröhlich, R. Israel, E.H. Lieb, B. Simon, Phase transitions and reflection positivity. I. General theory and long range lattice models
1978
Cited alongside, same era.
H. Kesten, The incipient infinite cluster in two-dimensional percolation , Probab. Theory Related Fields, 73(3):369–394, 1986
1986
Later among the works it cites.
M. Aizenman, D.J. Barsky, and R. Fernández, The phase transition
1987
Later among the works it cites.
J. Feldman, J. Magnen, V. Rivasseau, and R. Sénéor, Construction and Borel Summability of Infrared Φ 4 4 \Phi_{4}^{4} by a Phase Space Expansion
1987
Later among the works it cites.
T. Hara and H. Tasaki, A Rigorous Control of Logarithmic Corrections in Four-Dimensional ( ϕ 4 ) 4 (\phi_{4})^{4} Spin Systems. II. Critical Behaviour of Susceptibility and Correlation Length
1987
Later among the works it cites.
G.F. Lawler, Intersections of random walks , Modern Birkhäuser Classics, Birkhäuser/Springer, New York, 2013, Reprint of the 1996 edition
1996
Later among the works it cites.
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A.D. Sokal, Sokal, A.D.: A rigorous inequality for the specific heat of an Ising or ϕ 4 4 \phi_{4}^{4} ferromagnet. Phys. Lett. bf 71 A, 451–453 (1979)
1979
Cited alongside, same era.
E. H. Lieb, A refinement of Simon’s correlation inequality , Comm. Math. Phys. 77(2):127–135, 1980
1980
Cited alongside, same era.
B. Simon, Correlation inequalities and the decay of correlations in ferromagnets , Comm. Math. Phys. 77
1980
Cited alongside, same era.
M. Aizenman, Geometric analysis of φ 4 \varphi^{4} fields and Ising models. I, II , Comm. Math. Phys., 86(1):1–48, 1982
1982
Cited alongside, same era.
D. Brydges, J. Fröhlich, and T. Spencer, The random walk representation of classical spin systems and correlation inequalities , Comm. Math. Phys., 83(1):123–150, 1982
1982
Cited alongside, same era.
J. Fröhlich, On the triviality of λ ϕ d 4 \lambda\phi^{4}_{d} theories and the approach to the critical point in d > ( − ) 4 d_{\begin{subarray}{c}>\\ (-)\end{subarray}}4 dimensions , Nuclear Physics B, 200(2):281–296, 1982
1982
Cited alongside, same era.
A.D. Sokal, An alternate constructive approach to the ϕ 3 4 \phi^{4}_{3} quantum field theory, and a possible destructive approach to ϕ 4 4 \phi_{4}^{4} . , Ann. Inst. Henri Poincaré Phys. Théorique, 37:317–398, 1982
1982
Cited alongside, same era.
R. van der Hofstad and A. Járai, The incipient infinite cluster for high-dimensional unoriented percolation , J. Stat. Phys., 114(3-4):553–625, 2004
2004
Later among the works it cites.
G. Grimmett, The random-cluster model , Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 333, Springer-Verlag, Berlin, 2006
2006
Later among the works it cites.
A. Jaffe and E. Witten, Quantum Yang-Mills Theory , The millennium prize problems, (1):129, 2006, www.claymath.org/sites/default/files/yangmills.pdf
2006
Later among the works it cites.
M. Biskup, Reflection positivity and phase transitions in lattice spin models , Methods of contemporary mathematical statistical physics, Lecture Notes in Math., vol. 1970, Springer, Berlin, 2009, pp. 1–86
2009
Later among the works it cites.
R. Bauerschmidt, D.C. Brydges, and G. Slade, Scaling limits and critical behaviour of the 4-dimensional n n -component | ϕ 4 | |\phi^{4}| spin model
2014
Later among the works it cites.
M. Hairer, A theory of regularity structures
2014
Later among the works it cites.
M. Aizenman, H. Duminil-Copin, and V. Sidoravicius, Random Currents and Continuity of Ising Model’s Spontaneous Magnetization , Comm. Math. Phys., 334:719–742, 2015
2015
Later among the works it cites.
H. Duminil-Copin and V. Tassion, A new proof of the sharpness of the phase transition for Bernoulli percolation and the Ising model , Math. Phys., 343(2):725–745, 2016
2016
Later among the works it cites.
H. Duminil-Copin, Random currents expansion of the Ising model
2018
Later among the works it cites.
M. Aizenman, H. Duminil-Copin, V. Tassion and S. Warzel, Emergent Planarity in two-dimensional Ising Models with finite-range Interactions
2019
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H. Duminil-Copin, Lectures on the Ising and Potts models on the hypercubic lattice
2020
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H. Duminil-Copin, S. Goswami, and A. Raoufi, Exponential decay of truncated correlations for the Ising model in any dimension for all but the critical temperature
2020
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