Fetching the paper…
Reading the bibliography…
The diagonal spin-spin correlations $ \langle \sigma_{0,0}\sigma_{N,N} \rangle $ of the Ising model on a triangular lattice with general couplings in the three directions are evaluated in terms of a solution to a three-variable extension of the sixth Painlev\'e system, namely a Garnier system.
J. Malmquist, Sur les équations différentielles du second ordre dont l’intégrale générale a ses points critiques fixes , Arkiv Mat., Astron. Fys. 18
1922
Earlier work this paper cites.
K. Husimi and I. Syôzi, The statistics of honeycomb and triangular lattice. I , Progress Theoret. Physics 5
1950
Earlier work this paper cites.
G. F. Newell, Crystal statistics of a two-dimensional Ising lattice , Phys. Rev. 78
1950
Earlier work this paper cites.
by same author, Crystal statistics of a two-dimensional triangular Ising lattice , Physical Rev. (2) 79
1950
Earlier work this paper cites.
I. Syôzi, The statistics of honeycomb and triangular lattice. II , Progress Theoret. Physics 5
1950
Earlier work this paper cites.
H. N. V. Temperley, Statistical mechanics of the two-dimensional assembly , Proc. Roy. Soc. London. Ser. A. 202
1950
Earlier work this paper cites.
G. H. Wannier, Antiferromagnetism. The triangular Ising net , Physical Rev. (2) 79
1950
Earlier work this paper cites.
R. B. Potts, Combinatorial solution of the triangular Ising lattice , Proc. Phys. Soc. Sect. A. 68
1955
Earlier work this paper cites.
E. W. Montroll, R. B. Potts, and J. C. Ward, Correlations and spontaneous magnetization of the two-dimensional Ising model , J. Math. Phys. 4
1963
Earlier work this paper cites.
J. Stephenson, Ising-model spin correlations on the triangular lattice , J. Math. Phys. 5
1964
Earlier work this paper cites.
by same author, Ising model spin correlations on the triangular lattice. II. Fourth-order correlations , J. Math. Phys. 7
1966
Earlier work this paper cites.
by same author, Ising-model spin correlations on the triangular lattice. III. Isotropic antiferromagnetic lattice , J. Math. Phys. 11
1970
Earlier work this paper cites.
by same author, Ising-model spin correlations on the triangular lattice. IV. Anisotropic ferromagnetic and antiferromagnetic lattices , J. Math. Phys. 11
1970
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.
T. T. Wu, B. M. McCoy, C. A. Tracy, and E. Barouch, Spin-spin correlation functions for the two-dimensional Ising model: Exact theory in the scaling region , Phys. Rev. B 13
1976
Earlier work this paper cites.
M. Jimbo and T. Miwa, Deformation of linear ordinary differential equations. I , Proc. Japan Acad. Ser. A Math. Sci. 56
1980
Cited alongside, same era.
H. Kimura and K. Okamoto, On the polynomial Hamiltonian structure of the Garnier systems , J. Math. Pures Appl. (9) 63
1984
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
Cited alongside, same era.
V. N. Plechko, Grassmann path-integral solution for a class of triangular type decorated Ising models , Phys. A 152
1988
Cited alongside, same era.
N. A. Kostov, Quasi-periodic solutions of the integrable dynamical systems related to Hill’s equation , Lett. Math. Phys. 17
1989
Cited alongside, same era.
H. Sakai, Rational surfaces associated with affine root systems and geometry of the Painlevé equations , Comm. Math. Phys. 220
2001
Later among the works it cites.
H. Au-Yang and J. H. H. Perk, Correlation functions and susceptibility in the Z Z -invariant Ising model , MathPhys odyssey, 2001, Prog. Math. Phys., vol. 23, Birkhäuser Boston, Boston, MA, 2002, pp. 23–48. MR MR1903971 (2003i:82012)
2002
Later among the works it cites.
A. Borodin and P. Deift, Fredholm determinants, Jimbo-Miwa-Ueno τ \tau -functions, and representation theory , Comm. Pure Appl. Math. 55
2002
Later among the works it cites.
R. P. Millane, A. Goyal, and R. C. Penney, Ground states of the antiferromagnetic Ising model on finite triangular lattices of simple shape , Phys. Lett. A 311
2003
Later among the works it cites.
P. J. Forrester and N. S. Witte, Application of the tau-function theory of Painlevé equations to random matrices: P-VI, the JUE, CyUE, cJUE and scaled limits , Nagoya Math. J. 174
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
A. S. Fokas, A. R. It
1991
Cited alongside, same era.
K. Iwasaki, H. Kimura, S. Shimomura, and M. Yoshida, From Gauss to Painlevé , Aspects of Mathematics, E16, Friedr. Vieweg & Sohn, Braunschweig, 1991, A modern theory of special functions. MR MR1118604 (92j:33001)
1991
Cited alongside, same era.
T. Horiguchi, K. Tanaka, and T. Morita, Low-temperature behavior of antiferromagnetic Ising model on triangular lattice , J. Phys. Soc. Japan 61
1992
Cited alongside, same era.
G. Tondo, A connection between the Hénon-Heiles system and the Garnier system , Teoret. Mat. Fiz. 99
1994
Cited alongside, same era.
T. A. Ivanova and A. D. Popov, Some new integrable equations from the self-dual Yang-Mills equations , Phys. Lett. A 205
1995
Cited alongside, same era.
A. P. Magnus, Painlevé-type differential equations for the recurrence coefficients of semi-classical orthogonal polynomials , J. Comput. Appl. Math. 57
1995
Cited alongside, same era.
E. A. Bugriĭ, Solution of the 2 2 D Ising model on a triangular lattice by the auxiliary q q -deformed Grassmann field method , Theoret. Math. Phys. 109
1996
Cited alongside, same era.
2004
Later among the works it cites.
J. Zheng and G. Sun, Exact results for Ising models on the triangular Kagomé lattice , Phys. Rev. B 71
2005
Later among the works it cites.
N. D. Blakeley and R. P. Millane, Exact enumeration of the ground states of a triangular Ising antiferromagnet , Comput. Phys. Comm. 174
2006
Later among the works it cites.
by same author, Bi-orthogonal polynomials on the unit circle, regular semi-classical weights and integrable systems , Constr. Approx. 24
2006
Later among the works it cites.
N. S. Witte, Isomonodromic deformation theory and the next-to-diagonal correlations of the anisotropic square lattice Ising model , J. Phys. A: Math. Theor. 40
2007
Later among the works it cites.
Y. L. Loh, D.-X. Yao, and E. W. Carlson, Thermodynamics of Ising spins on the triangular Kagome lattice: Exact analytical method and Monte Carlo simulations , Physical Review B 77
2008
Later among the works it cites.
D.-X. Yao, Y. L. Loh, E. W. Carlson, and M. Ma, X X Z and Ising spins on the triangular Kagome lattice , Phys. Rev. B 78
2008
Later among the works it cites.
N. S. Witte, Bi-orthogonal systems on the unit circle, regular semi-classical weights and the discrete Garnier equations , Int. Math. Res. Not. 2009,
2009
Later among the works it cites.
D. H. Wojtas and R. P. Millane, Two-point correlation function for the triangular Ising antiferromagnet , Phys. Rev. E 79
2009
Later among the works it cites.
Y. Chan, A.J. Guttmann, B.G. Nickel, and J.H.H. Perk, The Ising susceptibility scaling function , J. Statist. Phys. 145
2011
Later among the works it cites.
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
Closest in time.