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Volumn 3, Issue , 2007, Pages

From holonomy of the ising model form factors to n-fold integrals and the theory of elliptic curves

Author keywords

Apparent singularities; Complete elliptic integrals; Complex multiplication; Elliptic representation of Painlev VI; Form factors; Fuchsian linear differential equations; Heegner numbers; Isogenies of elliptic curves; Landau singularities; Landen transformation; Modular forms; Moduli space of curves; Pinch singularities; Pointed curves; Scaling limit of the Ising model; Sigma form of Painlev VI; Singular behaviour; Susceptibility of the Ising model; Two point correlation functions of the lattice ising model

Indexed keywords


EID: 85032068739     PISSN: None     EISSN: 18150659     Source Type: Journal    
DOI: 10.3842/SIGMA.2007.099     Document Type: Article
Times cited : (1)

References (137)
  • 1
    • 0010787541 scopus 로고    scopus 로고
    • Moduli of Abelian varieties
    • Springer-Verlag, Heidelberg Berlin
    • Adler A., Ramanan S., Moduli of Abelian varieties, Lecture Notes in Mathematics, Vol. (1644), Springer-Verlag, Heidelberg Berlin, 1996.
    • (1996) Lecture Notes in Mathematics , vol.1644
    • Adler, A.1    Ramanan, S.2
  • 2
    • 0009675990 scopus 로고    scopus 로고
    • Correlation functions and susceptibility in the Z-invariant Ising model
    • Editors T. Miwa and M. Kashiwara, Birkhäuser, Boston
    • Au-Yang H., Perk J.H.H., Correlation functions and susceptibility in the Z-invariant Ising model, in Math-Phys Odyssee 2001: Integrable Models and Beyond, Editors T. Miwa and M. Kashiwara, Birkhäuser, Boston, 2002, 23-48.
    • (2002) Math-Phys Odyssee 2001: Integrable Models and Beyond , pp. 23-48
    • Au-Yang, H.1    Perk, J.H.H.2
  • 3
    • 0001940262 scopus 로고
    • Critical correlations in a Z-invariant inhomogeneous Ising model
    • Au-Yang H., Perk J.H.H., Critical correlations in a Z-invariant inhomogeneous Ising model, Phys. A 144 (1987), 44-104.
    • (1987) Phys. A , vol.144 , pp. 44-104
    • Au-Yang, H.1    Perk, J.H.H.2
  • 4
    • 0001370951 scopus 로고
    • Ising correlations at the critical temperature
    • see equation (4) on page 3
    • Au-Yang H., Perk J.H.H., Ising correlations at the critical temperature, Phys. Lett. A 104 (1984), 131-134, see equation (4) on page 3.
    • (1984) Phys. Lett. A , vol.104 , pp. 131-134
    • Au-Yang, H.1    Perk, J.H.H.2
  • 5
    • 0037142511 scopus 로고    scopus 로고
    • Star-triangle equations and identities in hypergeometric series, Internat
    • Au-Yang H., Perk J.H.H., Star-triangle equations and identities in hypergeometric series, Internat. J. Modern Phys. B 16 (2002), 1853-1865.
    • (2002) J. Modern Phys. B , vol.16 , pp. 1853-1865
    • Au-Yang, H.1    Perk, J.H.H.2
  • 6
    • 0009707151 scopus 로고    scopus 로고
    • Wavevector-dependent susceptibility in aperiodic planar Ising models
    • Editors T. Miwa and M. Kashiwara, Birkhäuser, Boston
    • Au-Yang H., Perk J.H.H., Wavevector-dependent susceptibility in aperiodic planar Ising models, in Math-Phys Odyssee 2001: Integrable Models and Beyond, Editors T. Miwa and M. Kashiwara, Birkḧauser, Boston, 2002, 1-21.
    • (2002) Math-Phys Odyssee 2001: Integrable Models and Beyond , pp. 1-21
    • Au-Yang, H.1    Perk, J.H.H.2
  • 7
    • 0001180950 scopus 로고
    • From form factors to correlation functions: The Ising model
    • Babelon O., Bernard D., From form factors to correlation functions: the Ising model, Phys. Lett. B 288 (1992), 113-120.
    • (1992) Phys. Lett. B , vol.288 , pp. 113-120
    • Babelon, O.1    Bernard, D.2
  • 12
    • 0001398970 scopus 로고
    • Solvable eight vertex model on an arbitrary planar lattice
    • Baxter R.J., Solvable eight vertex model on an arbitrary planar lattice, Phil. Trans. R. Soc. London A 289 (1978), 315-346.
    • (1978) Phil. Trans. R. Soc. London A , vol.289 , pp. 315-346
    • Baxter, R.J.1
  • 13
    • 0011630061 scopus 로고
    • Partition function of the eight-vertex lattice model
    • Baxter R.J., Partition function of the eight-vertex lattice model, Ann. Physics 70 (1972), 193-228.
    • (1972) Ann. Physics , vol.70 , pp. 193-228
    • Baxter, R.J.1
  • 14
    • 17744375725 scopus 로고
    • One-dimensional anisotropic Heisenberg chain
    • Baxter R.J., One-dimensional anisotropic Heisenberg chain, Ann. Physics 70 (1972), 323-337.
    • (1972) Ann. Physics , vol.70 , pp. 323-337
    • Baxter, R.J.1
  • 15
    • 0002152395 scopus 로고
    • Eight-vertex model in lattice statistics and one-dimensional anisotropic Heisenberg chain. I. Some fundamental eigenvectors
    • Baxter R.J., Eight-vertex model in lattice statistics and one-dimensional anisotropic Heisenberg chain. I. Some fundamental eigenvectors, Ann. Physics 76 (1973), 1-24.
    • (1973) Ann. Physics , vol.76 , pp. 1-24
    • Baxter, R.J.1
  • 16
    • 49549172862 scopus 로고
    • Eight-vertex model in lattice statistics and one-dimensional anisotropic Heisenberg chain. II. Equivalence to a generalized ice-type lattice model
    • Baxter R.J., Eight-vertex model in lattice statistics and one-dimensional anisotropic Heisenberg chain. II. Equivalence to a generalized ice-type lattice model, Ann. Physics 76 (1973), 25-47.
    • (1973) Ann. Physics , vol.76 , pp. 25-47
    • Baxter, R.J.1
  • 17
    • 49549168660 scopus 로고
    • Eight-vertex model in lattice statistics and one-dimensional anisotropic Heisenberg chain. III. Eigenvectors of the transfer matrix and the Hamiltonian
    • Baxter R.J., Eight-vertex model in lattice statistics and one-dimensional anisotropic Heisenberg chain. III. Eigenvectors of the transfer matrix and the Hamiltonian, Ann. Physics 76 (1973), 48-71.
    • (1973) Ann. Physics , vol.76 , pp. 48-71
    • Baxter, R.J.1
  • 18
    • 33748801761 scopus 로고    scopus 로고
    • The eight-vertex model and Painlevé VI, in Special Issue on Painlevé VI
    • hep-th/0602122
    • Bazhanov V.V., Mangazeev V.V., The eight-vertex model and Painlevé VI, in Special Issue on Painlevé VI, J. Phys. A: Math. Gen. 39 (2006), 12235-12243, hep-th/0602122.
    • (2006) J. Phys. A: Math. Gen. , vol.39 , pp. 12235-12243
    • Bazhanov, V.V.1    Mangazeev, V.V.2
  • 19
    • 0000590264 scopus 로고
    • Lattice Ising model in a field: E8 scattering theory
    • hep-th/9312169
    • Bazhanov V.V., Nienhuis B., Warnaar O., Lattice Ising model in a field: E8 scattering theory, Phys. Lett. B 322 (1994), 198-206, hep-th/9312169.
    • (1994) Phys. Lett. B , vol.322 , pp. 198-206
    • Bazhanov, V.V.1    Nienhuis, B.2    Warnaar, O.3
  • 20
    • 79952194765 scopus 로고    scopus 로고
    • VVariations de structure de Hodge, Variétés de Calabi-Yau et symétrie miroir
    • Bertin J., Peters C., Variations de structure de Hodge, Variétés de Calabi-Yau et symétrie miroir, Panorama et Synthèses, Vol. 3, Société Mathématique de France, 1996.
    • (1996) Panorama et Synthèses , vol.3
    • Bertin, J.1    Peters, C.2
  • 21
    • 0000356657 scopus 로고
    • A note on the irrationality of ξ(2) and ξ (3)
    • Beukers F., A note on the irrationality of ξ(2) and ξ (3), Bull. London Math. Soc. 11 (1979), 268-272.
    • (1979) Bull. London Math. Soc. , vol.11 , pp. 268-272
    • Beukers, F.1
  • 22
    • 34047094345 scopus 로고    scopus 로고
    • Motives associated to graphs
    • available at
    • Bloch S., Motives associated to graphs, Jpn. J. Math. 2 (2007), 165-196, available at http://math.bu.edu/people/kayeats/motives/graphrept061017.pdf.
    • (2007) Jpn. J. Math. , vol.2 , pp. 165-196
    • Bloch, S.1
  • 23
    • 49349127552 scopus 로고
    • Correlation-function identities for general Ising models
    • Boel R.J., Kasteleyn P.W., Correlation-function identities for general Ising models, Phys. A 93 (1978), 503-516.
    • (1978) Phys. A , vol.93 , pp. 503-516
    • Boel, R.J.1    Kasteleyn, P.W.2
  • 24
    • 34250279516 scopus 로고
    • Correlation-function identities and inequalities for Ising models with pair interactions
    • Boel R.J., Kasteleyn P.W., Correlation-function identities and inequalities for Ising models with pair interactions, Comm. Math. Phys. 161 (1978), 191-208.
    • (1978) Comm. Math. Phys. , vol.161 , pp. 191-208
    • Boel, R.J.1    Kasteleyn, P.W.2
  • 25
    • 0344237501 scopus 로고    scopus 로고
    • Evaluation of integrals representing correlations in the XXX Heisenberg spin chain
    • Editors M. Kashiwara and T. Miwa, Birkhäuser
    • Boos H.E., Korepin V.E., Evaluation of integrals representing correlations in the XXX Heisenberg spin chain, in MathPhys Odyssey (2001), Editors M. Kashiwara and T. Miwa, Birkhäuser, 2002, 65-108.
    • (2002) MathPhys Odyssey 2001 , pp. 65-108
    • Boos, H.E.1    Korepin, V.E.2
  • 26
    • 42749103019 scopus 로고    scopus 로고
    • Factorization of multiple integrals representing the density matrix of a finite segment of the Heisenberg spin chain, in The 75th Anniversary of the Bethe Ansatz
    • 13 pages
    • Boos H.E., Gohmann F., Klumper A., Suzuki J., Factorization of multiple integrals representing the density matrix of a finite segment of the Heisenberg spin chain, in The 75th Anniversary of the Bethe Ansatz, J. Stat. Mech. Theory Exp. 2006 (2006), P04001, 13 pages.
    • (2006) J. Stat. Mech. Theory Exp. , vol.2006
    • Boos, H.E.1    Gohmann, F.2    Klumper, A.3    Suzuki, J.4
  • 27
    • 0035816523 scopus 로고    scopus 로고
    • Quantum spin chains and Riemann zeta function with odd arguments
    • hep-th/0104008
    • Boos H.E., Korepin V.E., Quantum spin chains and Riemann zeta function with odd arguments, J. Phys. A: Math. Gen. 34 (2001), 5311-5316, hep-th/0104008.
    • (2001) J. Phys. A: Math. Gen. , vol.34 , pp. 5311-5316
    • Boos, H.E.1    Korepin, V.E.2
  • 31
    • 34547462820 scopus 로고    scopus 로고
    • Landau singularities and singularities of holonomic integrals of the Ising class
    • math-ph/0701016
    • Boukraa S., Hassani S., Maillard J.-M., Zenine N., Landau singularities and singularities of holonomic integrals of the Ising class, J. Phys. A: Math. Theor. 40 (2007), 2583-2614, math-ph/0701016.
    • (2007) J. Phys. A: Math. Theor. , vol.40 , pp. 2583-2614
    • Boukraa, S.1    Hassani, S.2    Maillard, J.-M.3    Zenine, N.4
  • 32
    • 35848950248 scopus 로고    scopus 로고
    • Singularities of n-fold integrals of the Ising class and the theory of elliptic curves
    • arXiv:0706.3367
    • Boukraa S., Hassani S., Maillard J.-M., Zenine N., Singularities of n-fold integrals of the Ising class and the theory of elliptic curves, J. Phys. A: Math. Theor. 40 (2007), 11713-11748, arXiv:0706.3367.
    • (2007) J. Phys. A: Math. Theor. , vol.40 , pp. 11713-11748
    • Boukraa, S.1    Hassani, S.2    Maillard, J.-M.3    Zenine, N.4
  • 34
    • 85012534453 scopus 로고    scopus 로고
    • Espaces de modules des courbes, groupes modulaires et théorie des champs
    • Numéro 7, Société Mathématique de France
    • Buff X., Fehrenbach J., Lochak P., Schnepps L., Vogel P., Espaces de modules des courbes, groupes modulaires et théorie des champs, Panorama et Synthèses, Numéro 7, Société Mathématique de France, 1999.
    • (1999) Panorama Et Synthèses
    • Buff, X.1    Fehrenbach, J.2    Lochak, P.3    Schnepps, L.4    Vogel, P.5
  • 35
    • 21344478290 scopus 로고
    • Ising model and n = 2 supersymmetric theories
    • hep-th/9209085
    • Cecotti S., Vafa C., Ising model and n = 2 supersymmetric theories, Comm. Math. Phys. 157 (1993), 139-178, hep-th/9209085.
    • (1993) Comm. Math. Phys. , vol.157 , pp. 139-178
    • Cecotti, S.1    Vafa, C.2
  • 38
    • 84889235517 scopus 로고
    • Dover Publishing Co., New York
    • Erdeleyi A., Asymptotic series, Dover Publishing Co., New York, (1956), p. 47.
    • (1956) Asymptotic Series , pp. 47
    • Erdeleyi, A.1
  • 39
    • 0003864328 scopus 로고
    • Bateman manuscript project, McGraw Hill, New York
    • Erdeleyi, Bateman manuscript project, higher transcendental functions, McGraw Hill, New York, 1955.
    • (1955) Higher Transcendental Functions
    • Erdeleyi1
  • 40
    • 0037340672 scopus 로고    scopus 로고
    • The Mori cones of moduli spaces of pointed curves of small genus
    • math.AG/0111268
    • Farkas G., Guibney A., The Mori cones of moduli spaces of pointed curves of small genus, Trans. Amer. Math. Soc. 355 (2003), 1183-1199, math.AG/0111268.
    • (2003) Trans. Amer. Math. Soc. , vol.355 , pp. 1183-1199
    • Farkas, G.1    Guibney, A.2
  • 42
    • 8744220536 scopus 로고    scopus 로고
    • Integrals of motion from TBA and lattice-conformal dictionary
    • hep-th/0405110
    • Feverati G., Grinza P., Integrals of motion from TBA and lattice-conformal dictionary, Nuclear Phys. B 702 (2004), 495-515, hep-th/0405110.
    • (2004) Nuclear Phys. B , vol.702 , pp. 495-515
    • Feverati, G.1    Grinza, P.2
  • 43
    • 85009837008 scopus 로고    scopus 로고
    • Groupes de Rhin-Viola et intégrales multiples
    • Fischler S., Groupes de Rhin-Viola et intégrales multiples, J. Théor. Nombres Bordeaux 15 (2003), 479-534.
    • (2003) J. Théor. Nombres Bordeaux , vol.15 , pp. 479-534
    • Fischler, S.1
  • 45
    • 33748741279 scopus 로고    scopus 로고
    • Irrationalité de valeurs de zêta (d'après Apéry, Rivoal)
    • math.NT/0303066
    • Fischler S., Irrationalité de valeurs de zêta (d'après Apéry, Rivoal), Séminaire Bourbaki, Exposé, no. 910, (2003), Ast́erisque 294 (2004), 27-62, math.NT/0303066.
    • (2004) Séminaire Bourbaki, Exposé, no. 910, 2003, Ast́erisque , vol.294 , pp. 27-62
    • Fischler, S.1
  • 46
    • 0040143107 scopus 로고
    • Sur les singularités irrégulières des équations différentielles linéaires
    • Garnier R., Sur les singularités irrégulières des équations différentielles linéaires, J. Math. Pures et Appl. 2 (1919), 99-198.
    • (1919) J. Math. Pures Et Appl. , vol.2 , pp. 99-198
    • Garnier, R.1
  • 47
    • 79952297982 scopus 로고    scopus 로고
    • Relative rigid cohomology and deformation of hypersurfaces
    • Art. ID rpm003, 67 pages
    • Gerkmann R., Relative rigid cohomology and deformation of hypersurfaces, Int. Math. Res. Pap. IMRP 2007 (2007), no. 1, Art. ID rpm003, 67 pages.
    • (2007) Int. Math. Res. Pap. IMRP , vol.2007
    • Gerkmann, R.1
  • 48
    • 0002331536 scopus 로고
    • Non-standard 2D critical statistical models from Liouville theory
    • Gervais J.-L., Neveu A., Non-standard 2D critical statistical models from Liouville theory, Nuclear Phys. B 257 (1985), 59-76.
    • (1985) Nuclear Phys B , vol.257 , pp. 59-76
    • Gervais, J.-L.1    Neveu, A.2
  • 49
    • 0032600934 scopus 로고    scopus 로고
    • Stokes operators via limit monodromy of generic perturbation
    • Glutsuk A.A., Stokes operators via limit monodromy of generic perturbation, J. Dynam. Control Systems 5 (1999), 101-135.
    • (1999) J. Dynam. Control Systems , vol.5 , pp. 101-135
    • Glutsuk, A.A.1
  • 50
    • 2942584516 scopus 로고    scopus 로고
    • 0,n
    • math.AG/0204102
    • Goncharov A.B., Manin Y., Multiple ζ-motives and moduli spaces M0,n, Comp. Math. 140 (2004), 1-14, math.AG/0204102.
    • (2004) Comp. Math. , vol.140 , pp. 1-14
    • Goncharov, A.B.1    Manin, Y.2
  • 51
    • 49349127206 scopus 로고
    • Correlation function identities for general planar Ising systems
    • Groeneveld J., Boel R.J., Kasteleyn P.W., Correlation function identities for general planar Ising systems, Phys. A 93 (1978), 138-154.
    • (1978) Phys. A , vol.93 , pp. 138-154
    • Groeneveld, J.1    Boel, R.J.2    Kasteleyn, P.W.3
  • 52
    • 0036350608 scopus 로고    scopus 로고
    • The elliptic representation of the general Painlevé VI equation
    • math.CV/0108073
    • Guzzetti D., The elliptic representation of the general Painlevé VI equation, Comm. Pure Appl. Math. 55 (2002), 1280-1363, math.CV/0108073.
    • (2002) Comm. Pure Appl. Math. , vol.55 , pp. 1280-1363
    • Guzzetti, D.1
  • 53
    • 33745311923 scopus 로고
    • The modular equations
    • Hanna M., The modular equations, Proc. London Math. Soc. 28 (1928), 46-52.
    • (1928) Proc. London Math. Soc. , vol.28 , pp. 46-52
    • Hanna, M.1
  • 55
    • 85043050642 scopus 로고    scopus 로고
    • Potential automorphy of odd-dimensional symmetric powers of elliptic curves, and applications, in Algebra, Arithmetic and Geometry - Manin Festschrift
    • Birkhäuser, to appear
    • Harris M., Potential automorphy of odd-dimensional symmetric powers of elliptic curves, and applications, in Algebra, Arithmetic and Geometry - Manin Festschrift, Progress in Mathematics, Birkhäuser, to appear.
    • Progress in Mathematics
    • Harris, M.1
  • 56
    • 0742281922 scopus 로고    scopus 로고
    • On the effective cone of the moduli space of pointed rational curves, in Topology and Geometry: Commemorating SISTAG
    • math.AG/0110231
    • Hassett B., Tschinkel Y., On the effective cone of the moduli space of pointed rational curves, in Topology and Geometry: Commemorating SISTAG, Contemp. Math. 314 (2002), 83-96, math.AG/0110231.
    • (2002) Contemp. Math. , vol.314 , pp. 83-96
    • Hassett, B.1    Tschinkel, Y.2
  • 57
    • 33748576259 scopus 로고    scopus 로고
    • Constructible sets of linear differential equations and effective rational approximations of polylogarithmic functions
    • Huttner M., Constructible sets of linear differential equations and effective rational approximations of polylogarithmic functions, Israel J. Math. 153 (2006), 1-44.
    • (2006) Israel J. Math. , vol.153 , pp. 1-44
    • Huttner, M.1
  • 59
    • 0007297810 scopus 로고
    • Inverse functional relations and disorder solutions on the Potts models
    • Jaekel M.T., Maillard J.-M., Inverse functional relations and disorder solutions on the Potts models, J. Phys. A: Math. Gen. 17 (1984), 2079-2094.
    • (1984) J. Phys. A: Math. Gen. , vol.17 , pp. 2079-2094
    • Jaekel, M.T.1    Maillard, J.-M.2
  • 60
    • 0342980998 scopus 로고
    • Inverse functional relations on the Potts model
    • Jaekel M.T., Maillard J.-M., Inverse functional relations on the Potts model, J. Phys. A: Math. Gen. 15 (1982), 2241-2257.
    • (1982) J. Phys. A: Math. Gen. , vol.15 , pp. 2241-2257
    • Jaekel, M.T.1    Maillard, J.-M.2
  • 61
    • 0346411612 scopus 로고
    • Difference equations in spin chains with a boundary
    • hep-th/9502060
    • Jimbo M., Kedem R., Konno H., Miwa T., Weston R., Difference equations in spin chains with a boundary, Nuclear Phys. B 448 (1995), 429-456, hep-th/9502060.
    • (1995) Nuclear Phys. B , vol.448 , pp. 429-456
    • Jimbo, M.1    Kedem, R.2    Konno, H.3    Miwa, T.4    Weston, R.5
  • 64
    • 21344473386 scopus 로고
    • Difference equations for the correlations of the eight vertex model
    • hep-th/9211066
    • Jimbo M., Miwa T., Nakayashiki A., Difference equations for the correlations of the eight vertex model, J. Phys. A: Math. Gen. 26 (1993), 2199-2209, hep-th/9211066.
    • (1993) J. Phys. A: Math. Gen. , vol.26 , pp. 2199-2209
    • Jimbo, M.1    Miwa, T.2    Nakayashiki, A.3
  • 65
    • 67651060641 scopus 로고
    • Introduction aux travaux récents de Dwork
    • (State Univ. New York, Stony Brook, New York, 1969), Amer. Math. Soc., Providence, R.I
    • Katz N.M., Introduction aux travaux récents de Dwork, in Proc. Sympos. Pure Math., Vol. XX (State Univ. New York, Stony Brook, New York, 1969), Amer. Math. Soc., Providence, R.I. 1971, 65-75.
    • (1971) Proc. Sympos. Pure Math. , vol.20 XX , pp. 65-75
    • Katz, N.M.1
  • 66
    • 51649183632 scopus 로고
    • Nilpotent connections and the monodromy theorem: Applications of a result of Turrittin
    • Katz N.M., Nilpotent connections and the monodromy theorem: applications of a result of Turrittin, Publications mathématiques de l'IHES 39 (1970), 175-232.
    • (1970) Publications Mathématiques De L'IHES , vol.39 , pp. 175-232
    • Katz, N.M.1
  • 67
    • 0002360958 scopus 로고
    • On the differential equations satisfied by period matrices
    • Katz N.M., On the differential equations satisfied by period matrices, Inst. Hautes Etudes Sci. Publ. Math. 35 (1968), 223-258.
    • (1968) Inst. Hautes Etudes Sci. Publ. Math. , vol.35 , pp. 223-258
    • Katz, N.M.1
  • 68
    • 0003362351 scopus 로고    scopus 로고
    • Rigid local systems
    • Princeton University press
    • Katz N.M., Rigid local systems, Ann. of Math. Stud., Vol. 139, Princeton University press, 1996.
    • (1996) Ann. of Math. Stud. , vol.139
    • Katz, N.M.1
  • 69
    • 0003222045 scopus 로고
    • Travaux de Dwork, in Séminaire Bourbaki (1971/1972), Exp. No. 409
    • Springer Verlag
    • Katz N.M., Travaux de Dwork, in Séminaire Bourbaki (1971/1972), Exp. No. 409, Lecture Notes in Math., Vol. 317, Springer Verlag, (1973), 167-200.
    • (1973) Lecture Notes in Math , vol.317 , pp. 167-200
    • Katz, N.M.1
  • 70
    • 36149015803 scopus 로고
    • Crystal statistics. II. Partition function evaluated by spinor analysis
    • Kaufman B., Crystal statistics. II. Partition function evaluated by spinor analysis, Phys. Rev. 76 (1949), 1232-1243.
    • (1949) Phys. Rev. , vol.76 , pp. 1232-1243
    • Kaufman, B.1
  • 71
    • 13844304606 scopus 로고
    • Short-range order in a binary Ising lattice
    • Kaufman B., Onsager L., Short-range order in a binary Ising lattice, Phys. Rev. 76 (1949), 1244-1252.
    • (1949) Phys. Rev. , vol.76 , pp. 1244-1252
    • Kaufman, B.1    Onsager, L.2
  • 72
    • 33845788645 scopus 로고    scopus 로고
    • An identity of Andrews, multiple integrals, and very-well-poised hypergeometric series
    • math.CA/0312148
    • Krattenthaler C., Rivoal T., An identity of Andrews, multiple integrals, and very-well-poised hypergeometric series, Ramanujan J. 13 (2007), 203-219, math.CA/0312148.
    • (2007) Ramanujan J. , vol.13 , pp. 203-219
    • Krattenthaler, C.1    Rivoal, T.2
  • 73
    • 0004291355 scopus 로고    scopus 로고
    • Knots and Feynman diagrams
    • Cambridge University Press, 2000, Chapter 9
    • Kreimer D., Knots and Feynman diagrams, Cambridge Lecture Notes in Physics, Vol. 13, Cambridge University Press, (2000), Chapter 9.
    • Cambridge Lecture Notes in Physics , vol.13
    • Kreimer, D.1
  • 76
    • 0030581204 scopus 로고    scopus 로고
    • Multi-point local height probabilities in the integrable RSOS model
    • hep-th/9602074
    • Lukyanov S., Pugai Y., Multi-point local height probabilities in the integrable RSOS model, Nuclear Phys. B 473 (1996), 631-658, hep-th/9602074.
    • (1996) Nuclear Phys. B , vol.473 , pp. 631-658
    • Lukyanov, S.1    Pugai, Y.2
  • 77
    • 34547478461 scopus 로고    scopus 로고
    • Form factor expansion of the row and diagonal correlation functions of the two dimensional using model
    • math-ph/0612051
    • Lyberg I., McCoy B.M., Form factor expansion of the row and diagonal correlation functions of the two dimensional using model, J. Phys. A: Math. Theor. 40 (2007), 3329-3346, math-ph/0612051.
    • (2007) J. Phys. A: Math. Theor. , vol.40 , pp. 3329-3346
    • Lyberg, I.1    McCoy, B.M.2
  • 79
    • 0022037227 scopus 로고
    • The inversion relation: Some simple examples
    • Maillard J.-M., The inversion relation: some simple examples, J. Physique 46 (1984), 329-341.
    • (1984) J. Physique , vol.46 , pp. 329-341
    • Maillard, J.-M.1
  • 80
    • 7544242403 scopus 로고    scopus 로고
    • Modular invariance in lattice statistical mechanics
    • Maillard J.-M., Boukraa S., Modular invariance in lattice statistical mechanics, Ann. Fond. Louis de Broglie 26 (2001), Special Issue 2, 287-328.
    • (2001) Ann. Fond. Louis De Broglie , vol.26 , Issue.2 SPCL. , pp. 287-328
    • Maillard, J.-M.1    Boukraa, S.2
  • 84
    • 0035599194 scopus 로고    scopus 로고
    • Picard and Chazy solutions to the Painlevé VI equation
    • math.AG/9901054
    • Mazzocco M., Picard and Chazy solutions to the Painlevé VI equation, Math. Ann. 321 (2001), 157-195, math.AG/9901054.
    • (2001) Math. Ann. , vol.321 , pp. 157-195
    • Mazzocco, M.1
  • 85
    • 0001343891 scopus 로고
    • Ising field theory: Quadratic difference equations for the n-point Green's functions on the lattice
    • McCoy B.M., Perk J.H.H., Wu T.T., Ising field theory: quadratic difference equations for the n-point Green's functions on the lattice, Phys. Rev. Lett. 46 (1981), 757-760.
    • (1981) Phys. Rev. Lett. , vol.46 , pp. 757-760
    • McCoy, B.M.1    Perk, J.H.H.2    Wu, T.T.3
  • 86
    • 36749106034 scopus 로고
    • Painlevé equations of the third kind
    • McCoy B., Tracy C.A., Wu T.T., Painlevé equations of the third kind, J. Math. Phys. 18 (1977), 1058-1092.
    • (1977) J. Math. Phys. , vol.18 , pp. 1058-1092
    • McCoy, B.1    Tracy, C.A.2    Wu, T.T.3
  • 87
    • 0000588657 scopus 로고
    • Nonlinear partial difference equations for the two-dimensional Ising model
    • McCoy B.M., Wu T.T., Nonlinear partial difference equations for the two-dimensional Ising model, Phys. Rev. Lett. 45 (1980), 675-678.
    • (1980) Phys. Rev. Lett. , vol.45 , pp. 675-678
    • McCoy, B.M.1    Wu, T.T.2
  • 90
    • 0033612075 scopus 로고    scopus 로고
    • On the singularity structure of the Ising model susceptibility
    • Nickel B., On the singularity structure of the Ising model susceptibility, J. Phys. A: Math. Gen. 32 (1999), 3889-3906.
    • (1999) J. Phys. A: Math. Gen. , vol.32 , pp. 3889-3906
    • Nickel, B.1
  • 91
    • 0001565059 scopus 로고    scopus 로고
    • Addendum to 'On the singularity structure of the Ising model susceptibility'
    • Nickel B., Addendum to 'On the singularity structure of the Ising model susceptibility', J. Phys. A: Math. Gen. 33 (2000), 1693-1711.
    • (2000) J. Phys. A: Math. Gen. , vol.33 , pp. 1693-1711
    • Nickel, B.1
  • 94
    • 34250120843 scopus 로고
    • Studies on the Painlevé equations. I. Sixth Painlevé equation P VI
    • Okamoto K., Studies on the Painlevé equations. I. Sixth Painlevé equation P VI, Ann. Mat. Pura Appl. (4) 146 (1987), 337-381.
    • (1987) Ann. Mat. Pura Appl. (4) , vol.146 , pp. 337-381
    • Okamoto, K.1
  • 95
    • 36149012281 scopus 로고
    • Crystal statistics. I. A two-dimensional model with an order disorder transition
    • Onsager L., Crystal statistics. I. A two-dimensional model with an order disorder transition, Phys. Rev. 65 (1944), 117-149.
    • (1944) Phys. Rev. , vol.65 , pp. 117-149
    • Onsager, L.1
  • 96
  • 97
    • 0035255923 scopus 로고    scopus 로고
    • The susceptibility of the square lattice Ising model: New developments
    • cond-mat/0103074
    • Orrick W.P., Nickel B.G., Guttmann A.J., Perk J.H.H., The susceptibility of the square lattice Ising model: new developments, J. Statist. Phys. 102 (2001), 795-841, cond-mat/0103074.
    • (2001) J. Statist. Phys. , vol.102 , pp. 795-841
    • Orrick, W.P.1    Nickel, B.G.2    Guttmann, A.J.3    Perk, J.H.H.4
  • 98
    • 0000433366 scopus 로고
    • Two-dimensional Ising correlations: Convergence of the scaling limit
    • Palmer J., Tracy C.A., Two-dimensional Ising correlations: convergence of the scaling limit, Adv. in Appl. Math. 2 (1981), 329-388.
    • (1981) Adv. in Appl. Math. , vol.2 , pp. 329-388
    • Palmer, J.1    Tracy, C.A.2
  • 99
    • 84857289800 scopus 로고
    • Temperley-Lieb operators and critical A-D-E models
    • Pearce P.A., Temperley-Lieb operators and critical A-D-E models, Internat. J. Modern Phys. A 4 (1990), 715-734.
    • (1990) Internat. J. Modern Phys. A , vol.4 , pp. 715-734
    • Pearce, P.A.1
  • 100
    • 0002275742 scopus 로고
    • Quadratic identities for Ising model correlations
    • Perk J.H.H., Quadratic identities for Ising model correlations, Phys. Lett. A 79 (1980), 3-5.
    • (1980) Phys. Lett. A , vol.79 , pp. 3-5
    • Perk, J.H.H.1
  • 101
    • 33745306887 scopus 로고    scopus 로고
    • Some recent results on pair correlation functions and susceptibilities in exactly solvable models, in Dunk Island Conference in Honor of 60th Birthday of A.J. Guttmann
    • math-ph/0606046
    • Perk J.H.H., Au-Yang H., Some recent results on pair correlation functions and susceptibilities in exactly solvable models, in Dunk Island Conference in Honor of 60th Birthday of A.J. Guttmann, J. Phys. Conf. Ser. 42 (2006), 231-238, math-ph/0606046.
    • (2006) J. Phys. Conf. Ser. , vol.42 , pp. 231-238
    • Perk, J.H.H.1    Au-Yang, H.2
  • 102
    • 0001188834 scopus 로고
    • Time-dependent xx-correlation functions in the one-dimensional XY -model
    • see equation (6.16)
    • Perk J.H.H., Capel H.W., Time-dependent xx-correlation functions in the one-dimensional XY -model, Phys. A 89 (1977), 265-303, see equation (6.16).
    • (1977) Phys. A , vol.89 , pp. 265-303
    • Perk, J.H.H.1    Capel, H.W.2
  • 103
    • 0000126711 scopus 로고
    • Mémoire sur la theorie des functions algébriques de deux variables
    • Picard E., Mémoire sur la theorie des functions algébriques de deux variables, Journal de Liouville 5 (1889), 135-319.
    • (1889) Journal De Liouville , vol.5 , pp. 135-319
    • Picard, E.1
  • 105
    • 11144342672 scopus 로고    scopus 로고
    • Doubles mélanges des polylogarithmes multiples aux racines de l'unité
    • math.QA/0202142
    • Racinet G., Doubles mélanges des polylogarithmes multiples aux racines de l'unité, Publ. Math. Inst. Hautes Études Sci. No. 95 (2002), 185-231, math.QA/0202142.
    • (2002) Publ. Math. Inst. Hautes Études Sci. , vol.95 , pp. 185-231
    • Racinet, G.1
  • 107
    • 35848945429 scopus 로고
    • Maillard J.-M., q-state Potts model on the checkerboard lattice
    • Rammal R., Maillard J.-M., q-state Potts model on the checkerboard lattice, J. Phys. A: Math. Gen. 16 (1983), 1073-1081.
    • (1983) J. Phys. A: Math. Gen. , vol.16 , pp. 1073-1081
    • Rammal, R.1
  • 108
    • 0001113681 scopus 로고
    • Some analytical consequences of the inverse relation for the Potts model
    • Rammal R., Maillard J.-M., Some analytical consequences of the inverse relation for the Potts model, J. Phys. A: Math. Gen. 16 (1983), 353-367.
    • (1983) J. Phys. A: Math. Gen. , vol.16 , pp. 353-367
    • Rammal, R.1    Maillard, J.-M.2
  • 110
    • 0035534919 scopus 로고    scopus 로고
    • Rational surfaces associated with affine root systems and geometry of the Painlevé equations
    • Sakai H., Rational surfaces associated with affine root systems and geometry of the Painlevé equations, Comm. Math. Phys. 220 (2001), 165-229.
    • (2001) Comm. Math. Phys. , vol.220 , pp. 165-229
    • Sakai, H.1
  • 111
    • 0035981821 scopus 로고    scopus 로고
    • 7 mass spectrum and the tricritical Ising model
    • math-ph/0110021
    • 7mass spectrum and the tricritical Ising model, J. Math. Phys. 43 (2002), 2636-2653, math-ph/0110021.
    • (2002) J. Math. Phys. , vol.43 , pp. 2636-2653
    • Seaton, K.A.1    Batchelor, M.T.2
  • 112
    • 0041523852 scopus 로고    scopus 로고
    • Testing reducibility of linear differential operators: A group theoretic perspective
    • Singer M.F., Testing reducibility of linear differential operators: a group theoretic perspective, Appl. Alg. Eng. Commun. Comp. 7 (1996), no. 2, 77-104.
    • (1996) Appl. Alg. Eng. Commun. Comp. , vol.7 , Issue.2 , pp. 77-104
    • Singer, M.F.1
  • 113
    • 0001811025 scopus 로고    scopus 로고
    • 2
    • 2, Mat. Sb. 187 (1996), no. 12, 87-120
    • (1996) Mat. Sb. , vol.187 , Issue.12 , pp. 87-120
    • Sorokin, V.N.1
  • 114
    • 0030299675 scopus 로고    scopus 로고
    • (English transl.)
    • English transl.: Sb. Math. 187 (1996), 1819-1852.
    • (1996) Sb. Math. , vol.187 , pp. 1819-1852
  • 115
    • 0038583254 scopus 로고    scopus 로고
    • Apéry's theorem, Vestnik Moskov
    • Sorokin V.N., Apéry's theorem, Vestnik Moskov. Univ. Ser. I Mat. Mekh. (1998), no. 3, 48-53, 74
    • (1998) Univ. Ser. I Mat. Mekh. , Issue.3 , pp. 48-53
    • Sorokin, V.N.1
  • 116
    • 0003193298 scopus 로고    scopus 로고
    • (English transl.)
    • English transl.: Moscow Univ. Math. Bull. 53 (1998), no. 3, 48-52.
    • (1998) Moscow Univ. Math. Bull. , vol.53 , Issue.3 , pp. 48-52
  • 118
    • 0031185987 scopus 로고    scopus 로고
    • On the confluence phenomenon of fuchsian equations
    • Sternin B.Yu., Shatalov V.E., On the confluence phenomenon of fuchsian equations, J. Dynam. Control Systems 3 (1997), 433-448.
    • (1997) J. Dynam. Control Systems , vol.3 , pp. 433-448
    • Sternin, B.Y.1    Shatalov, V.E.2
  • 119
    • 67651020281 scopus 로고
    • Arithmetic features of rational conformal field theory
    • Todorov I.T., Arithmetic features of rational conformal field theory, Ann. Inst. H. Poincaré 63 (1995), 427-453.
    • (1995) Ann. Inst. H. Poincaré , vol.63 , pp. 427-453
    • Todorov, I.T.1
  • 120
    • 0041459958 scopus 로고    scopus 로고
    • Galois theory of linear differential equations
    • Springer-Verlag, Berlin, available at
    • van der Put M., Singer M.F., Galois theory of linear differential equations, Grundlehren der Mathematischen Wissenschaften, Vol. 328, Springer-Verlag, Berlin, (2003), available at http://www4.ncsu.edu/singer/.
    • (2003) Grundlehren Der Mathematischen Wissenschaften , vol.328
    • van der Put, M.1    Singer, M.F.2
  • 121
    • 0030402125 scopus 로고    scopus 로고
    • Rational solutions of the mixed differential equation and its application to factorization of differential operators
    • ACM, New York
    • van Hoeij M., Rational solutions of the mixed differential equation and its application to factorization of differential operators, in Proceedings ISSAC'96, ACM, New York, (1996), 219-225.
    • (1996) Proceedings ISSAC'96 , pp. 219-225
    • van Hoeij, M.1
  • 122
  • 123
    • 9944254696 scopus 로고    scopus 로고
    • Some formulas for Riemann zeta-function at integer points, Vestnik Moskov
    • Vasilyev D.V., Some formulas for Riemann zeta-function at integer points, Vestnik Moskov. Univ. Ser. I Mat. Mekh. (1996), no. 1, 81-84
    • (1996) Univ. Ser. I Mat. Mekh. , vol.1 , pp. 81-84
    • Vasilyev, D.V.1
  • 124
    • 30244544057 scopus 로고    scopus 로고
    • (English transl.)
    • English transl.: Moscow Univ. Math. Bull. 51 (1996), no. 1, 41-43.
    • (1996) Moscow Univ. Math. Bull. , vol.51 , Issue.1 , pp. 41-43
  • 125
    • 0000368688 scopus 로고
    • New construction of solvable lattice models including an Ising model in a field
    • Warnaar O., Nienhuis B., Seaton K.A., New construction of solvable lattice models including an Ising model in a field, Phys. Rev. Lett. 69 (1992), 710-712.
    • (1992) Phys. Rev. Lett. , vol.69 , pp. 710-712
    • Warnaar, O.1    Nienhuis, B.2    Seaton, K.A.3
  • 128
    • 34250219967 scopus 로고    scopus 로고
    • Isomonodromic deformation theory and the next-to-diagonal correlations of the anisotropic square lattice Ising model
    • arXiv:0705.0557
    • Witte N.S., Isomonodromic deformation theory and the next-to-diagonal correlations of the anisotropic square lattice Ising model, J. Phys. A: Math. Theor. 40 (2007), F491-F501, arXiv:0705.0557.
    • (2007) J. Phys. A: Math. Theor. , vol.40
    • Witte, N.S.1
  • 129
    • 0000812425 scopus 로고
    • Theory of Toeplitz determinants and of the spin correlations of the two-dimensional Ising model
    • Wu T.T., Theory of Toeplitz determinants and of the spin correlations of the two-dimensional Ising model, Phys. Rev. 149 (1966), 380-440.
    • (1966) Phys. Rev. , vol.149 , pp. 380-440
    • Wu, T.T.1
  • 130
    • 0000715867 scopus 로고
    • Spin-spin correlation functions for the two dimensional Ising model: Exact theory in the scaling region
    • Wu T.T., McCoy B.M., Tracy C.A., Barouch E., Spin-spin correlation functions for the two dimensional Ising model: exact theory in the scaling region, Phys. Rev. B 13 (1976), 316-374.
    • (1976) Phys. Rev. B , vol.13 , pp. 316-374
    • Wu, T.T.1    McCoy, B.M.2    Tracy, C.A.3    Barouch, E.4
  • 131
    • 0001526186 scopus 로고
    • On the spin-spin correlation function of the Ising square lattice and the zero field susceptibility
    • Yamada K., On the spin-spin correlation function of the Ising square lattice and the zero field susceptibility, Progr. Theoret. Phys. 71 (1984), 1416-1418.
    • (1984) Progr. Theoret. Phys. , vol.71 , pp. 1416-1418
    • Yamada, K.1
  • 132
    • 36149022411 scopus 로고
    • The spontaneous magnetization of the two dimensional Ising model
    • Yang C.N., The spontaneous magnetization of the two dimensional Ising model, Physical Rev. (2) 85 (1952), 808-816.
    • (1952) Physical Rev. (2) , vol.85 , pp. 808-816
    • Yang, C.N.1
  • 133
    • 7544224049 scopus 로고    scopus 로고
    • The Fuchsian differential equation of the square Ising model χ(3) susceptibility
    • math-ph/0407060
    • Zenine N., Boukraa S., Hassani S., Maillard J.M., The Fuchsian differential equation of the square Ising model χ(3) susceptibility, J. Phys. A: Math. Gen. 37 (2004), 9651-9668, math-ph/0407060.
    • (2004) J. Phys. A: Math. Gen. , vol.37 , pp. 9651-9668
    • Zenine, N.1    Boukraa, S.2    Hassani, S.3    Maillard, J.M.4
  • 134
    • 18744407059 scopus 로고    scopus 로고
    • Ising model susceptibility: Fuchsian differential equation for χ(4) and its factorization properties
    • cond-mat/0502155
    • Zenine N., Boukraa S., Hassani S., Maillard J.M., Ising model susceptibility: Fuchsian differential equation for χ(4) and its factorization properties, J. Phys. A: Math. Gen. 38 (2005), 4149-4173, cond-mat/0502155.
    • (2005) J. Phys. A: Math. Gen. , vol.38 , pp. 4149-4173
    • Zenine, N.1    Boukraa, S.2    Hassani, S.3    Maillard, J.M.4
  • 135
    • 26844459130 scopus 로고    scopus 로고
    • Square lattice Ising model susceptibility: Connection matrices and singular behavior of χ (3) and χ (4)
    • hep-th/0506214, math-ph/0506065
    • Zenine N., Boukraa S., Hassani S., Maillard J.M., Square lattice Ising model susceptibility: connection matrices and singular behavior of χ (3) and χ (4), J. Phys. A: Math. Gen. 38 (2005), 9439-9474, hep-th/0506214, math-ph/0506065.
    • (2005) J. Phys. A: Math. Gen. , vol.38 , pp. 9439-9474
    • Zenine, N.1    Boukraa, S.2    Hassani, S.3    Maillard, J.M.4
  • 136
    • 14844320097 scopus 로고    scopus 로고
    • Square lattice Ising model susceptibility: Series expansion method, and differential equation for χ (3)
    • hep-ph/0411051
    • Zenine N., Boukraa S., Hassani S., Maillard J.M., Square lattice Ising model susceptibility: series expansion method, and differential equation for χ (3), J. Phys. A: Math. Gen. 38 (2005), 1875-1899, hep-ph/0411051.
    • (2005) J. Phys. A: Math. Gen. , vol.38 , pp. 1875-1899
    • Zenine, N.1    Boukraa, S.2    Hassani, S.3    Maillard, J.M.4
  • 137
    • 2342449626 scopus 로고    scopus 로고
    • Confluence et phénomènes de Stokes
    • Zhang C., Confluence et phénomènes de Stokes, J. Math. Sci. Univ. Tokyo 3 (1996), 91-107.
    • (1996) J. Math. Sci. Univ. Tokyo , vol.3 , pp. 91-107
    • Zhang, C.1


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