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In 1980 Jimbo and Miwa evaluated the diagonal two-point correlation function of the square lattice Ising model as a $\tau$-function of the sixth Painlev\'e system by constructing an associated isomonodromic system within their theory of holonomic quantum fields.
G. Szegö, Orthogonal polynomials , third ed., Colloquium Publications 23
1967
Earlier work this paper cites.
B. McCoy and T. T. Wu, The Two-Dimensional Ising Model , Harvard University Press, Harvard, 1973
1973
Earlier work this paper cites.
M. Jimbo and T. Miwa, Studies on holonomic quantum fields. XVII , Proc. Japan Acad. Ser. A Math. Sci. 56
1980
Earlier work this paper cites.
L. P. Kadanoff and M. Kohmoto, SMJ’s analysis of Ising model correlation functions , Ann. Physics 126
1980
Earlier work this paper cites.
M. Sato, T. Miwa, and M. Jimbo, Aspects of holonomic quantum fields. Isomonodromic deformation and Ising model , Complex analysis, microlocal calculus and relativistic quantum theory (Proc. Internat. Colloq., Centre Phys., Les Houches, 1979), Lecture Notes in Phys., vol. 126, Springer, Berlin, 1980, pp. 429–491. MR MR579762 (86j:81078)
1980
Earlier work this paper cites.
by same author, Errata , Proc. Japan Acad. Ser. A Math. Sci. 57
1981
Earlier work this paper cites.
R. J. Baxter, Exactly Solved Models in Statistical Mechanics , Academic Press, London, 1982
1982
Cited alongside, same era.
T. Miwa and M. Jimbo, Introduction to Holonomic Quantum Fields , The Riemann problem, complete integrability and arithmetic applications (Bures-sur-Yvette/New York, 1979/1980), Lecture Notes in Math., vol. 925, Springer, Berlin, 1982, pp. 28–36
1982
Cited alongside, same era.
R. K. Ghosh and R. E. Shrock, Exact expressions for diagonal correlation functions in the d = 2 d=2 Ising model , Phys. Rev. B (3) 30
1984
Cited alongside, same era.
H. Au-Yang and J. H. H. Perk, Critical correlations in a Z Z -invariant inhomogeneous Ising model , Phys. A 144
1987
Cited alongside, same era.
K. Okamoto, Studies on the Painlevé equations. I. Sixth Painlevé equation P VI {P}_{{\rm{V}{I}}} , Ann. Mat. Pura Appl. (4) 146
1987
A. Borodin, Discrete gap probabilities and discrete Painlevé equations , Duke Math. J. 117
2003
Later among the works it cites.
P. J. Forrester and N. S. Witte, Application of the τ \tau -function theory of Painlevé equations to random matrices: P VI {\rm P}_{\rm VI} , the JUE, CyUE, cJUE and scaled limits , Nagoya Math. J. 174
2004
Later among the works it cites.
by same author, Bi-orthogonal Polynomials on the Unit Circle, regular semi-classical Weights and Integrable Systems , Construct. Approx. 24
2006
Later among the works it cites.
J. Palmer, Planar Ising Correlations and the Deformation Analysis of Scaling , Progress in Mathematical Physics, 2007
2007
Closest in time.
N. S. Witte, Bi-orthogonal Polynomials on the Unit Circle, regular semi-classical Weights and Integrable Systems - II. , 2007
2007
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Cited alongside, same era.
H. Au-Yang, B.-Q. Jin, and J. H. H. Perk, Wavevector-dependent susceptibility in quasiperiodic Ising models , Proceedings of the Baxter Revolution in Mathematical Physics (Canberra, 2000), vol. 102, 2001, pp. 501–543. MR MR1832062 (2002c:82013)
2001
Cited alongside, same era.
P. J. Forrester, Log Gases and Random Matrices , http://www.ms.unimelb.edu.au/ ~ \tilde{\,} matpjf/matpjf.html
Cited in the paper.
by same author, Discrete Painlevé equations for a class of P VI P_{\rm VI} τ \tau -functions given as U ( N ) {\rm U}(N) averages , Nonlinearity 18
2088
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