. Limite-thermodynamique, 82 CHAPITRE 7. CONCLUSION ET PERSPECTIVES ? Article X : A. Caradoc , O. Foda , N. Kitanine, Higher spin vertex models with domain wall boundary conditions, J. Stat. Mech, vol.03012, pp.math-ph, 2006.

?. Article and X. Kitanine, Correlation functions of the XXX Heisenberg higher spin chains, J. Phys. A, vol.34, issue.8151, p.104016, 2001.

?. Article, X. Kitanine, J. Kozlowski, G. Maillet, N. Niccoli et al., Correlation functions of the open XXZ chain I

]. M. Bibliographie1, D. J. Ablowitz, A. C. Kaup, H. Newell, and . Segur, Nonlinear-evolution equations of physical significance, Phys. Rev. Lett, vol.31, issue.2, pp.125-127, 1973.

M. J. Ablowitz, D. J. Kaup, A. C. Newell, and H. Segur, The Inverse Scattering Transform-Fourier Analysis for Nonlinear Problems, Studies in Applied Mathematics, vol.34, issue.12, pp.249-315, 1974.
DOI : 10.1002/sapm1974534249

I. Affleck, Exact correlation amplitude for the S = 1

F. C. Alcaraz, M. N. Barber, M. T. Batchelor, R. J. Baxter, and G. R. , Surface exponents of the quantum XXZ, Ashkin-Teller and Potts models, Journal of Physics A: Mathematical and General, vol.20, issue.18, pp.6397-6409, 1987.
DOI : 10.1088/0305-4470/20/18/038

O. Babelon, H. J. De, C. Vega, and . Viallet, Analysis of the Bethe ansatz equations of the XXZ model, Nuclear Physics B, vol.220, issue.1, pp.13-34, 1983.
DOI : 10.1016/0550-3213(83)90131-1

H. M. Babujian, Exact solution of the isotropic Heisenberg chain with arbitrary spins: Thermodynamics of the model, Nuclear Physics B, vol.215, issue.3, pp.317-336, 1983.
DOI : 10.1016/0550-3213(83)90668-5

E. Barnes, The theory of the G-function, Quart. J. Math, vol.31, pp.264-314, 1899.

E. Barouch and B. M. Mccoy, Model. II. Spin-Correlation Functions, Physical Review A, vol.3, issue.2, pp.786-804, 1971.
DOI : 10.1103/PhysRevA.3.786

V. Barzykin and I. Affleck, Finite-size scaling for the spin-1

R. Baxter, Partition function of the Eight-Vertex lattice model, Annals of Physics, vol.70, issue.1, pp.193-228, 1972.
DOI : 10.1016/0003-4916(72)90335-1

R. J. Baxter, Spontaneous staggered polarization of the F model, Journal of Physics C: Solid State Physics, vol.6, issue.5, pp.145-182, 1973.
DOI : 10.1088/0022-3719/6/5/004

R. J. Baxter, Corner transfer matrices of the eight-vertex model. I. Low-temperature expansions and conjectured properties, Journal of Statistical Physics, vol.76, issue.6, pp.485-503, 1976.
DOI : 10.1007/BF01020802

R. J. Baxter, Corner transfer matrices of the eight-vertex model. II. The Ising model case, Journal of Statistical Physics, vol.11, issue.1, pp.1-14, 1977.
DOI : 10.1007/BF01089373

R. J. Baxter, Exactly Solved Models in Statistical Mechanics, 1982.
DOI : 10.1142/9789814415255_0002

A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov, Infinite conformal symmetry in two dimensional quantum field theory Hidden Yangians in 2D massive current algebras, Nucl. Phys. Comm. Math. Phys, vol.241, issue.1371, pp.333-380191, 1984.

D. Bernard, AN INTRODUCTION TO YANGIAN SYMMETRIES, International Journal of Modern Physics B, vol.07, issue.20n21, pp.3517-3530, 1993.
DOI : 10.1142/S0217979293003371

H. Bethe, Zur Theorie der Metalle, Zeitschrift f???r Physik, vol.71, issue.3-4, pp.205-226, 1931.
DOI : 10.1007/BF01341708

N. M. Bogoliubov, A. G. Izergin, and N. Y. Reshetikhin, Finite-size effects and infrared asymptotics of the correlation functions in two dimensions, Journal of Physics A: Mathematical and General, vol.20, issue.15, pp.5361-5369, 1987.
DOI : 10.1088/0305-4470/20/15/047

H. Boos, M. Jimbo, T. Miwa, F. Smirnov, and Y. Takeyama, A recursion formula for the correlation functions of an inhomogeneous XXX model, Algebra i Analiz, vol.17, issue.1, pp.115-159, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00101481

H. Boos, M. Jimbo, T. Miwa, F. Smirnov, and Y. Takeyama, Traces on the Sklyanin algebra and correlation functions of the eight-vertex model, Journal of Physics A: Mathematical and General, vol.38, issue.35, pp.387629-7659, 2005.
DOI : 10.1088/0305-4470/38/35/003
URL : https://hal.archives-ouvertes.fr/hal-00101478

H. Boos, M. Jimbo, T. Miwa, F. Smirnov, and Y. Takeyama, Algebraic Representation of Correlation Functions in Integrable Spin Chains, Annales Henri Poincar??, vol.7, issue.7-8, pp.1395-1428, 2006.
DOI : 10.1007/s00023-006-0285-5
URL : https://hal.archives-ouvertes.fr/hal-00101476

H. Boos, M. Jimbo, T. Miwa, F. Smirnov, and Y. Takeyama, Density Matrix of a Finite Sub-chain of the Heisenberg Anti-ferromagnet, Letters in Mathematical Physics, vol.658, issue.3, pp.201-208, 2006.
DOI : 10.1007/s11005-006-0054-x
URL : https://hal.archives-ouvertes.fr/hal-00101477

H. Boos, M. Jimbo, T. Miwa, F. Smirnov, and Y. Takeyama, Reduced qKZ Equation and Correlation Functions of the XXZ Model, Communications in Mathematical Physics, vol.261, issue.1, pp.245-276, 2006.
DOI : 10.1007/s00220-005-1430-6
URL : https://hal.archives-ouvertes.fr/hal-00101479

H. Boos, M. Jimbo, T. Miwa, F. Smirnov, and Y. Takeyama, Fermionic basis for space of operators in the XXZ model. hep-th, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00169335

H. Boos, V. Korepin, and F. Smirnov, New formulae for solutions of quantum Knizhnik???Zamolodchikov equations on level-4, Special issue on recent advances in the theory of quantum integrable systems, pp.323-335, 2004.
DOI : 10.1088/0305-4470/37/2/004

H. E. Boos and V. E. Korepin, Quantum spin chains and Riemann zeta function with odd arguments, Journal of Physics A: Mathematical and General, vol.34, issue.26, pp.5311-5316, 2001.
DOI : 10.1088/0305-4470/34/26/301
URL : http://arxiv.org/abs/hep-th/0104008

H. E. Boos, V. E. Korepin, Y. Nishiyama, and M. Shiroishi, Quantum correlations and number theory, Journal of Physics A: Mathematical and General, vol.35, issue.20, pp.354443-4451, 2002.
DOI : 10.1088/0305-4470/35/20/305
URL : http://arxiv.org/abs/cond-mat/0202346

H. E. Boos, V. E. Korepin, and F. A. Smirnov, Emptiness formation probability and quantum Knizhnik???Zamolodchikov equation, Nuclear Physics B, vol.658, issue.3, pp.417-439, 2003.
DOI : 10.1016/S0550-3213(03)00153-6

A. H. Bougourzi and R. A. Weston, N-point correlation functions of the spin-1 XXZ model, Nuclear Physics B, vol.417, issue.3, pp.439-462, 1994.
DOI : 10.1016/0550-3213(94)90480-4

D. M. Bressoud, Proofs and confirmations. MAA Spectrum The story of the alternating sign matrix conjecture, 1999.
DOI : 10.1017/cbo9780511613449

A. Caradoc, O. Foda, and N. Kitanine, Higher spin vertex models with domain wall boundary conditions, Journal of Statistical Mechanics: Theory and Experiment, vol.2006, issue.03, p.3012, 2006.
DOI : 10.1088/1742-5468/2006/03/P03012
URL : https://hal.archives-ouvertes.fr/hal-00171157

J. S. Caux, R. Hagemans, and J. M. Maillet, Computation of dynamical correlation functions of Heisenberg chains: the gapless anisotropic regime, Journal of Statistical Mechanics: Theory and Experiment, vol.2005, issue.09, p.9003, 2005.
DOI : 10.1088/1742-5468/2005/09/P09003
URL : https://hal.archives-ouvertes.fr/ensl-00266543

J. S. Caux and J. M. Maillet, Computation of Dynamical Correlation Functions of Heisenberg Chains in a Magnetic Field, Physical Review Letters, vol.95, issue.7, p.77201, 2005.
DOI : 10.1103/PhysRevLett.95.077201

I. V. Cherednik, Factorizing particles on a half-line and root systems, Theoretical and Mathematical Physics, vol.5, issue.1, pp.977-983, 1984.
DOI : 10.1007/BF01038545

F. Colomo, A. G. Izergin, V. E. Korepin, and V. Tognetti, Correlators in the Heisenberg XX0 chain as Fredholm determinants, Phys. Lett. A, vol.169, pp.237-247, 1992.

F. Colomo, A. G. Izergin, V. E. Korepin, and V. Tognetti, Temperature correlation functions in the XX0 Heisenberg chain. I, Theoretical and Mathematical Physics, vol.31, issue.1, pp.19-38, 1993.
DOI : 10.1007/BF01016992

D. Creamer, H. Thacker, and D. Wilkinson, Some exact results for the two-point function of an integrable quantum field theory, Physical Review D, vol.23, issue.12, pp.3081-3084, 1981.
DOI : 10.1103/PhysRevD.23.3081

H. De-vega, H. Eichenherr, and J. Maillet, Classical and quantum algebras of non-local charges in ?? models, Communications in Mathematical Physics, vol.200, issue.4, pp.507-524, 1984.
DOI : 10.1007/BF01215281

H. De-vega, H. Eichenherr, and J. Maillet, Yang-Baxter algebras of monodromy matrices in integrable quantum field theories, Nuclear Physics B, vol.240, issue.3, pp.240-377, 1984.
DOI : 10.1016/0550-3213(84)90272-4

H. J. De and . Vega, Integrable vertex models and extended conformal invariance, J. Phys. A, vol.21, issue.22, pp.1089-1095, 1988.

P. , D. Francesco, and P. Zinn-justin, Around the Razumov-Stroganov conjecture : proof of a multi-parameter sum rule, Electron. J. Combin.Research Paper, vol.12, issue.27, p.pp, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00004601

P. , D. Francesco, and P. Zinn-justin, The quantum Knizhnik-Zamolodchikov equation , generalized Razumov-Stroganov sum rules and extended Joseph polynomials

L. Faddeev and L. Takhtajan, Hamiltonian methods in the theory of solitons, 1987.
DOI : 10.1007/978-3-540-69969-9

L. D. Faddeev, INTEGRABLE MODELS IN (1 + 1)-DIMENSIONAL QUANTUM FIELD THEORY, Les Houches 1982, Recent advances in field theory and statistical mechanics, pp.561-608, 1984.
DOI : 10.1142/9789812815453_0009

L. D. Faddeev, E. K. Sklyanin, and L. A. Takhtajan, Quantum inverse problem method I. Theor What is the spin of a spin wave ?, Math. Phys. Phys. Lett. A, vol.40, issue.85, pp.688-7066, 1979.

I. B. Frenkel and N. Y. Reshetikhin, Quantum affine algebras and holonomic difference equations, Communications in Mathematical Physics, vol.3, issue.[FS2], pp.1-60, 1992.
DOI : 10.1007/BF02099206

D. Friedan, E. Martinec, and S. Shenker, Conformal invariance, supersymmetry and string theory, Nuclear Physics B, vol.271, issue.3-4, pp.93-165, 1986.
DOI : 10.1016/S0550-3213(86)80006-2
URL : http://doi.org/10.1016/0550-3213(86)90356-1

C. S. Gardner, J. M. Greene, M. D. Kruskal, and R. M. Miura, Method for Solving the Korteweg-deVries Equation, Physical Review Letters, vol.19, issue.19, pp.1095-1097, 1967.
DOI : 10.1103/PhysRevLett.19.1095

M. Gaudin, La fonction d'onde de Bethe, 1983.

M. Gaudin, B. M. Mccoy, and T. T. Wu, Normalization sum for the Bethe's hypothesis wave functions of the Heisenberg-Ising chain, Physical Review D, vol.23, issue.2, pp.417-419, 1981.
DOI : 10.1103/PhysRevD.23.417

S. Ghoshal and A. Zamolodchikov, BOUNDARY S MATRIX AND BOUNDARY STATE IN TWO-DIMENSIONAL INTEGRABLE QUANTUM FIELD THEORY, International Journal of Modern Physics A, vol.09, issue.21, pp.3841-3885, 1994.
DOI : 10.1142/S0217751X94001552

F. Göhmann, A. Klümper, and A. Seel, chain at finite temperature, Journal of Physics A: Mathematical and General, vol.37, issue.31, pp.7625-7651, 2004.
DOI : 10.1088/0305-4470/37/31/001

F. Göhmann, A. Klümper, and A. Seel, Integral representation of the density matrix of the XXZ chain at finite temperatures, Journal of Physics A: Mathematical and General, vol.38, issue.9, pp.1833-1841, 2005.
DOI : 10.1088/0305-4470/38/9/001

W. Heisenberg, Zur Theorie der Ferromagnetismus, pp.619-636, 1928.
DOI : 10.1007/978-3-642-61659-4_35

L. Hulthén, Uber das austauschproblem eines kristalles, Arkiv Mat. Astron. Fysik, vol.26, pp.1-106, 1938.

E. Ising, Beitrag zur Theorie des Ferromagnetismus, Zeitschrift f??r Physik, vol.6, issue.4, pp.253-258, 1925.
DOI : 10.1007/BF02980577

A. Its, A. Izergin, and V. Korepin, Correlation radius for one-dimensional impenetrable bosons, Physics Letters A, vol.141, issue.3-4, pp.121-124, 1989.
DOI : 10.1016/0375-9601(89)90771-8

A. Its, A. Izergin, and V. Korepin, Long-distance asymptotics of temperature correlators of the impenetrable Bose gas, Communications in Mathematical Physics, vol.1, issue.3, pp.471-488, 1990.
DOI : 10.1007/BF02096932

A. Its, A. Izergin, and V. Korepin, Temperature correlators of the impenetrable Bose gas as an integrable system, Communications in Mathematical Physics, vol.25, issue.1, pp.205-222, 1990.
DOI : 10.1007/BF02096786

A. Its, A. Izergin, and V. Korepin, Space correlations in the one-dimensional impenetrable Bose gas at finite temperature, Physica D: Nonlinear Phenomena, vol.53, issue.1, p.181, 1991.
DOI : 10.1016/0167-2789(91)90171-5

A. Its, A. Izergin, V. Korepin, and N. Slavnov, DIFFERENTIAL EQUATIONS FOR QUANTUM CORRELATION FUNCTIONS, International Journal of Modern Physics B, vol.04, issue.05, pp.1003-1037, 1990.
DOI : 10.1142/S0217979290000504

A. Its, A. Izergin, V. Korepin, and N. Slavnov, Temperature correlations of quantum spins, Physical Review Letters, vol.70, issue.11, pp.1704-1706, 1993.
DOI : 10.1103/PhysRevLett.70.1704

A. Its, A. Izergin, V. Korepin, and G. Varguzin, Large time and distance asymptotics of field correlation function of impenetrable bosons at finite temperature, Physica D: Nonlinear Phenomena, vol.54, issue.4, pp.351-395, 1992.
DOI : 10.1016/0167-2789(92)90043-M

A. Its and N. Slavnov, On the Riemann-Hilbert approach to the asymptotic analysis of the correlation functions of the quantum nonlinear Schrodinger equation. Non-free fermionic case. preprint MI-98-76, math-ph, 1998.

C. Itzykson, H. Saleur, and J. Zuber, Conformal invariance and applications to statistical mechanics, World Scintific, 1988.
DOI : 10.1142/0608

A. G. Izergin, Partition function of the six-vertex model in a finite volume, Sov. Phys. Dokl, vol.32, pp.878-879, 1987.

A. G. Izergin, N. Kitanine, J. M. Maillet, and V. Terras, Spontaneous magnetization of the XXZ Heisenberg chain, Nuclear Physics B, vol.554, issue.3, pp.679-696, 1999.
DOI : 10.1016/S0550-3213(99)00273-4

A. G. Izergin and V. E. Korepin, The quantum inverse scattering method approach to correlation functions, Communications in Mathematical Physics, vol.34, issue.1, pp.67-92, 1984.
DOI : 10.1007/BF01212350

A. G. Izergin and V. E. Korepin, Correlation functions for the Heisenberg XXZ-antiferromagnet, Communications in Mathematical Physics, vol.60, issue.2, pp.271-302, 1985.
DOI : 10.1007/BF01212283

A. G. Izergin, V. E. Korepin, and N. Y. Reshetikhin, Conformal dimensions in Bethe ansatz solvable models, Journal of Physics A: Mathematical and General, vol.22, issue.13, pp.222615-2620, 1989.
DOI : 10.1088/0305-4470/22/13/052

M. Jimbo, and the Yang???Baxter Equation, Lett. Math. Phys, vol.10, pp.63-69, 1985.
DOI : 10.1142/9789812798336_0015

M. Jimbo, A q-analogue of U(g[(N+1)), Hecke algebra, and the Yang-Baxter equation, Letters in Mathematical Physics, vol.40, issue.3, pp.247-252, 1986.
DOI : 10.1007/BF00400222

M. Jimbo, R. Kedem, T. Kojima, H. Konno, and T. Miwa, XXZ chain with a boundary, Nuclear Physics B, vol.441, issue.3, pp.437-470, 1995.
DOI : 10.1016/0550-3213(95)00062-W

M. Jimbo, K. Miki, T. Miwa, and A. Nakayashiki, Correlation functions of the XXZ model for ?? < ??? 1, Physics Letters A, vol.168, issue.4, pp.256-263, 1992.
DOI : 10.1016/0375-9601(92)91128-E

M. Jimbo and T. Miwa, Algebraic analysis of solvable lattice models, 1995.
DOI : 10.1090/cbms/085
URL : http://cds.cern.ch/record/263995/files/P00023727.pdf

M. Jimbo and T. Miwa, model in the gapless regime, Journal of Physics A: Mathematical and General, vol.29, issue.12, pp.2923-2958, 1996.
DOI : 10.1088/0305-4470/29/12/005

M. Jimbo, T. Miwa, Y. Môri, and M. Sato, Density matrix of an impenetrable Bose gas and the fifth Painlev?? transcendent, Physica D: Nonlinear Phenomena, vol.1, issue.1, pp.80-158, 1980.
DOI : 10.1016/0167-2789(80)90006-8

J. D. Johnson, S. Krinsky, and B. M. Mccoy, Hamiltonian, Physical Review A, vol.8, issue.5, pp.2526-2547, 1973.
DOI : 10.1103/PhysRevA.8.2526

M. Karowski, XIII. Exact S-matrices and form factors in 1 + 1 dimensional field theoretic models with soliton behaviour, Physics Reports, vol.49, issue.2, pp.229-237, 1979.
DOI : 10.1016/0370-1573(79)90113-3

M. Karowski and P. Weisz, Exact form factors in (1 + 1)-dimensional field theoretic models with soliton behaviour, Nuclear Physics B, vol.139, issue.4, pp.455-476, 1978.
DOI : 10.1016/0550-3213(78)90362-0

B. Kaufman, Crystal Statistics. II. Partition Function Evaluated by Spinor Analysis, Physical Review, vol.76, issue.8, pp.1232-1243, 1949.
DOI : 10.1103/PhysRev.76.1232

A. N. Kirillov and N. Y. Reshetikhin, Exact solution of the Heisenberg XXZ model of spin s, Journal of Soviet Mathematics, vol.61, issue.No. 3, pp.145109-133, 1985.
DOI : 10.1007/BF01083768

A. N. Kirillov and N. Y. Reshetikhin, Exact solution of the integrable XXZ Heisenberg model with arbitrary spin. I. The ground state and the excitation spectrum, Journal of Physics A: Mathematical and General, vol.20, issue.6
DOI : 10.1088/0305-4470/20/6/038

A. N. Kirillov and N. Y. Reshetikhin, Exact solution of the integrable XXZ Heisenberg model with arbitrary spin. II. Thermodynamics of the system, Journal of Physics A: Mathematical and General, vol.20, issue.6, pp.1587-1597, 1987.
DOI : 10.1088/0305-4470/20/6/039

N. Kitanine, chains, Journal of Physics A: Mathematical and General, vol.34, issue.39, pp.8151-8169, 2001.
DOI : 10.1088/0305-4470/34/39/314
URL : https://hal.archives-ouvertes.fr/tel-00175290

N. Kitanine, K. Kozlowski, J. M. Maillet, G. Niccoli, N. A. Slavnov et al., chain: I, Journal of Statistical Mechanics: Theory and Experiment, vol.2007, issue.10, pp.hep- th, 2007.
DOI : 10.1088/1742-5468/2007/10/P10009
URL : https://hal.archives-ouvertes.fr/ensl-00266468

N. Kitanine, J. M. Maillet, N. Slavnov, and V. Terras, spin-1/2 Heisenberg chain, Journal of Physics A: Mathematical and General, vol.35, issue.49, p.753, 2002.
DOI : 10.1088/0305-4470/35/49/102
URL : https://hal.archives-ouvertes.fr/hal-00369146

N. Kitanine, J. M. Maillet, N. Slavnov, and V. Terras, Spin???spin correlation functions of the XXZ- Heisenberg chain in a magnetic field, Nuclear Physics B, vol.641, issue.3, pp.487-518, 2002.
DOI : 10.1016/S0550-3213(02)00583-7

N. Kitanine, J. M. Maillet, N. A. Slavnov, and V. Terras, Correlation functions of the XXZ spin-1
URL : https://hal.archives-ouvertes.fr/ensl-00266560

N. Kitanine, J. M. Maillet, N. A. Slavnov, and V. Terras, Emptiness formation probability of the XXZ spin-1

N. Kitanine, J. M. Maillet, N. A. Slavnov, and V. Terras, Dynamical correlation functions of the spin- chain, Nuclear Physics B, vol.729, issue.3, pp.558-580, 2005.
DOI : 10.1016/j.nuclphysb.2005.08.046
URL : https://hal.archives-ouvertes.fr/ensl-00266560

N. Kitanine, J. M. Maillet, N. A. Slavnov, and V. Terras, chain at ?? = 1/2, Journal of Statistical Mechanics: Theory and Experiment, vol.2005, issue.09, p.9002, 2005.
DOI : 10.1088/1742-5468/2005/09/L09002

N. Kitanine, J. M. Maillet, N. A. Slavnov, and V. Terras, Master equation for spin???spin correlation functions of the chain, Nuclear Physics B, vol.712, issue.3, pp.600-622, 2005.
DOI : 10.1016/j.nuclphysb.2005.01.050
URL : https://hal.archives-ouvertes.fr/ensl-00266563

N. Kitanine, J. M. Maillet, N. A. Slavnov, and V. Terras, On the spin-spin correlation functions of the XXZ spin-1
URL : https://hal.archives-ouvertes.fr/ensl-00266561

N. Kitanine, J. M. Maillet, and V. Terras, Form factors of the XXZ Heisenberg finite chain, Nuclear Physics B, vol.554, issue.3, pp.647-678, 1999.
DOI : 10.1016/S0550-3213(99)00295-3

N. Kitanine, J. M. Maillet, and V. Terras, Spin???spin correlation functions of the XXZ- Heisenberg chain in a magnetic field, Nuclear Physics B, vol.641, issue.3, pp.554-582, 2000.
DOI : 10.1016/S0550-3213(02)00583-7

T. Kojima, V. E. Korepin, and N. A. Slavnov, Completely Integrable Equation for the Quantum Correlation Function of Nonlinear Schr??dinger Equation, Communications in Mathematical Physics, vol.189, issue.3, pp.709-728, 1997.
DOI : 10.1007/s002200050226

T. Kojima, V. E. Korepin, and N. A. Slavnov, Determinant Representation for Dynamical Correlation Functions of the Quantum Nonlinear Schr??dinger Equation, Communications in Mathematical Physics, vol.188, issue.3, pp.657-689, 1997.
DOI : 10.1007/s002200050182

V. Korepin, A. Izergin, F. Essler, and D. Uglov, Correlation function of the spin- XXX antiferromagnet, Physics Letters A, vol.190, issue.2, pp.182-184, 1994.
DOI : 10.1016/0375-9601(94)90074-4

V. Korepin, S. Lukyanov, Y. Nishiyama, and M. Shiroishi, Asymptotic behavior of the emptiness formation probability in the critical phase of XXZ spin chain, Physics Letters A, vol.312, issue.1-2
DOI : 10.1016/S0375-9601(03)00616-9

V. E. Korepin, Calculation of norms of Bethe wave functions, Communications in Mathematical Physics, vol.289, issue.1, pp.391-418, 1982.
DOI : 10.1007/BF01212176

V. E. Korepin, Dual field formulation of quantum integrable models, Communications in Mathematical Physics, vol.257, issue.2, pp.177-190, 1987.
DOI : 10.1007/BF01223510

V. E. Korepin, N. M. Bogoliubov, and A. G. Izergin, Quantum inverse scattering method and correlation functions, 1993.
DOI : 10.1090/trans2/201/08
URL : http://arxiv.org/abs/cond-mat/9301031

H. A. Kramers and G. H. Wannier, Statistics of the Two-Dimensional Ferromagnet. Part II, Physical Review, vol.60, issue.3, pp.263-276, 1941.
DOI : 10.1103/PhysRev.60.263

P. Kulish, Quantum difference nonlinear Schr???dinger equation, Letters in Mathematical Physics, vol.95, issue.3, pp.191-197, 1981.
DOI : 10.1007/BF00420698

P. Kulish and N. Reshetikhin, Quantum linear problem for the sine-Gordon equation and higher representations, Journal of Soviet Mathematics, vol.32, issue.No. 2, pp.2435-2441, 1983.
DOI : 10.1007/BF01084171

P. P. Kulish, N. Y. Reshetikhin, and E. K. Sklyanin, Yang-Baxter equation and representation theory: I, Letters in Mathematical Physics, vol.99, issue.5, pp.393-403, 1981.
DOI : 10.1007/BF02285311

P. P. Kulish and E. K. Sklyanin, Quantum inverse scattering method and the Heisenberg ferromagnet, Physics Letters A, vol.70, issue.5-6, pp.5-6461, 1979.
DOI : 10.1016/0375-9601(79)90365-7

G. Kuperberg, Another proof of the alternating sign matrix conjecture, Internat. Math. Res. Notices, pp.139-150, 1996.

G. Kuperberg, Symmetry Classes of Alternating-Sign Matrices under One Roof, The Annals of Mathematics, vol.156, issue.3, pp.835-866, 2002.
DOI : 10.2307/3597283

P. Lax, Integrals of nonlinear equations of evolution and solitary waves, Communications on Pure and Applied Mathematics, vol.15, issue.5, pp.467-490, 1968.
DOI : 10.1002/cpa.3160210503

A. Leclair and F. Smirnov, INFINITE QUANTUM GROUP SYMMETRY OF FIELDS IN MASSIVE 2D QUANTUM FIELD THEORY, International Journal of Modern Physics A, vol.07, issue.13, pp.2997-3022, 1992.
DOI : 10.1142/S0217751X92001332

A. Lenard, Momentum Distribution in the Ground State of the One???Dimensional System of Impenetrable Bosons, Journal of Mathematical Physics, vol.5, issue.7, pp.930-943, 1964.
DOI : 10.1063/1.1704196

A. E. Lenard, T. Lieb, D. Schultz, and . Mattis, One-dimensional impenetrable bosons in thermal equilibrium [118] E. Lieb. Residual entropy of square ice Two soluble models of an antiferromagnetic chain, J. Math. Phys. Phys. Rev. Ann. Phys, vol.7119, issue.16, pp.1268-1272162, 1961.

E. Lieb and F. Wu, Absence of Mott Transition in an Exact Solution of the Short-Range, One-Band Model in One Dimension, Physical Review Letters, vol.20, issue.25, pp.1445-1448, 1968.
DOI : 10.1103/PhysRevLett.20.1445

E. H. Lieb, Exact Analysis of an Interacting Bose Gas. II. The Excitation Spectrum, Physical Review, vol.130, issue.4, pp.1616-1624, 1963.
DOI : 10.1103/PhysRev.130.1616

E. H. Lieb and W. Liniger, Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State, Physical Review, vol.130, issue.4, pp.1605-1616, 1963.
DOI : 10.1103/PhysRev.130.1605

S. Lukyanov, spin chain in the disordered regime, Physical Review B, vol.59, issue.17, pp.11163-11164, 1999.
DOI : 10.1103/PhysRevB.59.11163

S. Lukyanov and V. Terras, Long-distance asymptotics of spin???spin correlation functions for the XXZ spin chain, Nuclear Physics B, vol.654, issue.3, pp.323-356, 2003.
DOI : 10.1016/S0550-3213(02)01141-0
URL : https://hal.archives-ouvertes.fr/hal-00366445

M. Lüscher, Quantum non-local charges and absence of particle production in the two-dimensional non-linear ??-model, Nuclear Physics B, vol.135, issue.1, pp.1-19, 1978.
DOI : 10.1016/0550-3213(78)90211-0

J. M. Maillet, J. Sanchez-de, and S. , Drinfel ? d twists and algebraic Bethe ansatz, 's Seminar on Mathematical Physics Amer. Math. Soc. Transl. Ser, vol.201, issue.2, pp.137-178, 2000.
DOI : 10.1090/trans2/201/10
URL : http://arxiv.org/abs/q-alg/9612012

J. M. Maillet and V. Terras, On the quantum inverse scattering problem, Nuclear Physics B, vol.575, issue.3, pp.627-644, 2000.
DOI : 10.1016/S0550-3213(00)00097-3

B. Mccoy, Model, Physical Review, vol.173, issue.2, pp.531-541, 1968.
DOI : 10.1103/PhysRev.173.531

B. Mccoy, E. Barouch, and D. Abraham, Model. IV. Time-Dependent Spin-Correlation Functions, Physical Review A, vol.4, issue.6, pp.2331-2341, 1971.
DOI : 10.1103/PhysRevA.4.2331

B. Mccoy and T. Wu, The Two-Dimensional lsing Model, 1973.

W. H. Mills, D. P. Robbins, H. Rumsey, and J. , Alternating sign matrices and descending plane partitions, Journal of Combinatorial Theory, Series A, vol.34, issue.3, pp.340-359, 1983.
DOI : 10.1016/0097-3165(83)90068-7
URL : http://doi.org/10.1016/0097-3165(83)90068-7

S. Mitra, B. Nienhuis, J. De-gier, and M. T. Batchelor, Exact expressions for correlations in the ground state of the dense O(1) loop model, Journal of Statistical Mechanics: Theory and Experiment, vol.2004, issue.09, p.9010, 2004.
DOI : 10.1088/1742-5468/2004/09/P09010

G. F. Newell and E. W. , On the Theory of the Ising Model of Ferromagnetism, Reviews of Modern Physics, vol.25, issue.2, pp.353-389, 1953.
DOI : 10.1103/RevModPhys.25.353

L. Onsager, Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition, Physical Review, vol.65, issue.3-4, pp.117-149, 1944.
DOI : 10.1103/PhysRev.65.117

R. Orbach, Linear Antiferromagnetic Chain with Anisotropic Coupling, Physical Review, vol.112, issue.2, pp.309-316, 1958.
DOI : 10.1103/PhysRev.112.309

V. Pasquier, Incompressible Representations of the Birman-Wenzl-Murakami Algebra, Annales Henri Poincar??, vol.7, issue.4, pp.603-619, 2006.
DOI : 10.1007/s00023-006-0262-z

P. A. Pearce, V. Rittenberg, and J. De-gier, Critical q=1 Potts model and Temperley-Lieb stochastic processes, 2001.
DOI : 10.1088/0305-4470/35/45/105
URL : http://arxiv.org/abs/math-ph/0209017

P. A. Pearce, V. Rittenberg, J. De-gier, and B. Nienhuis, Temperley??Lieb stochastic processes, Journal of Physics A: Mathematical and General, vol.35, issue.45, pp.661-668, 2002.
DOI : 10.1088/0305-4470/35/45/105
URL : http://arxiv.org/abs/math-ph/0209017

A. V. Razumov and Y. G. Stroganov, Spin chains and combinatorics, Journal of Physics A: Mathematical and General, vol.34, issue.14, pp.3185-3190, 2001.
DOI : 10.1088/0305-4470/34/14/322
URL : http://arxiv.org/abs/cond-mat/0012141

A. V. Razumov and Y. G. Stroganov, Spin chains and combinatorics: twisted boundary conditions, Journal of Physics A: Mathematical and General, vol.34, issue.26, pp.5335-5340, 2001.
DOI : 10.1088/0305-4470/34/26/304
URL : http://arxiv.org/abs/cond-mat/0102247

A. V. Razumov and Y. G. Stroganov, Combinatorial Nature of the Ground-State Vector of the O(1) Loop Model, Theoretical and Mathematical Physics, vol.138, issue.3, pp.395-400, 2004.
DOI : 10.1023/B:TAMP.0000018450.36514.d7

A. V. Razumov and Y. G. Stroganov, $O(1)$ loop model with different boundary conditions and symmetry classes of alternating-sign matrices, Teoreticheskaya i Matematicheskaya Fizika, vol.142, issue.2, pp.284-292, 2005.
DOI : 10.4213/tmf1782

K. Sakai, Dynamical correlation functions of the XXZ model at finite temperature. cond-mat/0703319, 2007.

J. Sato, M. Shiroishi, and M. Takahashi, Correlation functions of the spin- antiferromagnetic Heisenberg chain: Exact calculation via the generating function, Nuclear Physics B, vol.729, issue.3, pp.441-466, 2005.
DOI : 10.1016/j.nuclphysb.2005.08.045

M. Sato, T. Miwa, and M. Jimbo, Holonomic quantum fields. III, Publications of the Research Institute for Mathematical Sciences, vol.15, issue.2, pp.577-629, 1979.
DOI : 10.2977/prims/1195188185

M. Sato, T. Miwa, and M. Jimbo, Holonomic quantum fields. V, Publications of the Research Institute for Mathematical Sciences, vol.16, issue.2, pp.531-584, 1980.
DOI : 10.2977/prims/1195187216

M. Shiroishi, M. Takahashi, and Y. Nishiyama, Model, Journal of the Physical Society of Japan, vol.70, issue.12, pp.3535-3543, 2001.
DOI : 10.1143/JPSJ.70.3535

E. Sklyanin, On complete integrability of the Landau-Lifshitz equation, 1979.

E. Sklyanin, Boundary conditions for integrable quantum systems, Journal of Physics A: Mathematical and General, vol.21, issue.10, pp.2375-2389, 1988.
DOI : 10.1088/0305-4470/21/10/015

S. Skorik and A. Kapustin, Surface excitations and surface energy of the antiferromagnetic XXZ chain by the bethe ansatz approach, J. Phys. A, vol.29, pp.1629-1638, 1996.

S. Skorik and H. Saleur, Boundary bound states and boundary bootstrap in the sine-Gordon model with Dirichlet boundary conditions, Journal of Physics A: Mathematical and General, vol.28, issue.23, pp.6605-6622, 1995.
DOI : 10.1088/0305-4470/28/23/014

N. A. Slavnov, Calculation of scalar products of wave functions and form factors in the framework of the alcebraic Bethe ansatz, Theoretical and Mathematical Physics, vol.164, issue.2, pp.502-508, 1989.
DOI : 10.1007/BF01016531

F. A. Smirnov, The quantum Gelfand-Levitan-Marchenko equations and form factors in the sine-Gordon model, Journal of Physics A: Mathematical and General, vol.17, issue.16, pp.873-878356, 1984.
DOI : 10.1088/0305-4470/17/16/003

F. A. Smirnov, Reductions of the sine-Gordon model as a perturbation of minimal models of conformal field theory, Nuclear Physics B, vol.337, issue.1, pp.156-180, 1990.
DOI : 10.1016/0550-3213(90)90255-C

B. Sutherland, Exact Solution of a Two-Dimensional Model for Hydrogen-Bonded Crystals, Physical Review Letters, vol.19, issue.3, pp.103-104, 1967.
DOI : 10.1103/PhysRevLett.19.103

M. Takahashi, Half-filled Hubbard model at low temperature, Journal of Physics C: Solid State Physics, vol.10, issue.8, pp.1289-7301, 1977.
DOI : 10.1088/0022-3719/10/8/031

L. A. Takhtadzhan and L. D. Faddeev, The quantum method of the inverse problem and the heisenberg XY Z model, Uspekyi Mat. Nauk, vol.34, pp.13-63, 1979.

L. A. Takhtadzhyan and L. D. Faddeev, Essentially nonlinear one-dimensional model of classical field theory, Theoretical and Mathematical Physics, vol.262, issue.No. 4, pp.1046-1057, 1974.
DOI : 10.1007/BF01035551

L. A. Takhtadzhyan and L. D. Faddeev, The spectrum and scattering of excitations in the one-dimensional isotropic Heisenberg model Differential geometry, Lie groups and mechanics, Zap. Nauchn. Sem. LOMI, vol.109, issue.184, pp.134-178, 1981.

L. A. Takhtajan, Integration of the continuous Heisenberg spin chain through the inverse scattering method, Physics Letters A, vol.64, issue.2, pp.235-237, 1977.
DOI : 10.1016/0375-9601(77)90727-7

L. A. Takhtajan, The picture of low-lying excitations in the isotropic Heisenberg chain of arbitrary spins, Physics Letters A, vol.87, issue.9, pp.479-48282, 1981.
DOI : 10.1016/0375-9601(82)90764-2

V. Tarasov and A. Varchenko, Asymptotic solutions to the quantized Kniznik- Zamolodchikov equation and Bethe vectors, Amer. Math. Society Transl, vol.174, issue.2, pp.235-273, 1996.

V. Terras, Drinfel ? d twists and functional Bethe ansatz, Letters in Mathematical Physics, vol.48, issue.3, pp.263-276, 1999.
DOI : 10.1023/A:1007695001683

O. Tsuchiya, Determinant formula for the six-vertex model with reflecting end, Journal of Mathematical Physics, vol.39, issue.11, pp.5946-5951, 1998.
DOI : 10.1063/1.532606

L. R. Walker, Antiferromagnetic Linear Chain, Physical Review, vol.116, issue.5, pp.1089-1090, 1959.
DOI : 10.1103/PhysRev.116.1089

Y. Wang, The reconstruction of local quantum operators for the boundary XXZ spin-1

Y. Wang, The scalar products and the norm of Bethe eigenstates for the boundary XXX Heisenberg spin-1/2 finite chain, Nuclear Physics B, vol.622, issue.3, pp.633-649, 2002.
DOI : 10.1016/S0550-3213(01)00610-1

F. Woynarovich, =0 excited states of an anisotropic Heisenberg chain, Journal of Physics A: Mathematical and General, vol.15, issue.9, pp.2985-2996, 1982.
DOI : 10.1088/0305-4470/15/9/044

T. T. Wu, Theory of Toeplitz Determinants and the Spin Correlations of the Two-Dimensional Ising Model. I, Physical Review, vol.149, issue.1, pp.380-401, 1966.
DOI : 10.1103/PhysRev.149.380

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, Physical Review B, vol.13, issue.1, pp.316-374, 1976.
DOI : 10.1103/PhysRevB.13.316

C. Yang and C. Yang, One-Dimensional Chain of Anisotropic Spin-Spin Interactions. I. Proof of Bethe's Hypothesis for Ground State in a Finite System, Physical Review, vol.150, issue.1, pp.321-327, 1966.
DOI : 10.1103/PhysRev.150.321

C. N. Yang, Some Exact Results for the Many-Body Problem in one Dimension with Repulsive Delta-Function Interaction, Physical Review Letters, vol.19, issue.23, pp.1312-1315, 1967.
DOI : 10.1103/PhysRevLett.19.1312

C. N. Yang and C. P. Yang, One-Dimensional Chain of Anisotropic Spin-Spin Interactions. II. Properties of the Ground-State Energy Per Lattice Site for an Infinite System, Physical Review, vol.150, issue.1, pp.327-339, 1966.
DOI : 10.1103/PhysRev.150.327

V. E. Zakharov and L. D. Faddeev, The Korteweg-de Vries equation is a fully integrable Hamiltonian system, Funkcional. Anal. i Prilo?en, vol.5, issue.4, pp.18-27, 1971.

V. E. Zakharov and A. B. Shabat, Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media (differential equation solution for plane self focusing and one dimensional self modulation of waves interacting in nonlinear media), Soviet Physics-JETP, vol.34, pp.62-69, 1972.

V. E. Zakharov, L. A. Takhtadzhyan, and L. D. Faddeev, Complete description of solutions of the " sine-Gordon " equation, Soviet Physics Doklady, vol.19, p.822, 1975.

A. B. Zamolodchikov and V. A. Fateev, A model factorized S-matrix and an integrable spin-1 Heisenberg chain, Soviet J. Nuclear Phys, vol.32, pp.581-590, 1980.

A. B. Zamolodchikov and A. B. Zamolodchikov, Factorized S-matrices in two dimensions as the exact solutions of certain relativistic quantum field theory models

D. Zeilberger, Proof of the alternating sign matrix conjecture. Electron The Foata Festschrift, Research Paper 13, approx. 84 pp. (electronic), 1996.