Abstract
From the work of the Part I we are now in a position to address ourselves to the main problem posed in these lectures — the evaluation of Z, (1.11), for the s-G field after canonical transformation to the action-angle variables (4.27).
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References
R.J. Baxter: Exactly Solved Models in Statistical Mechanics (Academic Press 1982).
L.D. Faddeev, L.A. Takhtadzhyan: Usepekhi Mat. Nauk. 34, 13 (1979).
P.P. Kulish, E.K. Sklyanin: “Quantum Spectral Transform Method. Recent Developments”, in Proc. of the Tvärminne Symposium, Finland, 1981. J. Hietarinta and C. Montonen eds. (Springer Verlag, Heidelberg 1982).
J. Weiss, M. Tabor, G. Carnevale: J. Math. Phys. 24, 522 (1983); J. Weiss:
J. Math. Phys. 24, 1405 (1983). (In the event the Painlevé property was not mentioned at the School).
L.D. Faddeev: in Proc. Ecole d’Eté de Physique Theorique, Les Houches 1982 R. Stora and J.B. Zuber eds, (North Holland, Amsterdam 1983).
H.B. Thacker: Rev. od. Phys. 53, 253 (1981).
M. Fowler, X. Zotos: Phys. Rev. B24, 2634 (1981).
M. Imada, K. Hida, M. Ishikawa: J. Phys. C16, 35 (1983).
R.K. Bullough: in Bifurcation Phenomena in Mathematical Physics (D. Reidel Publ. Co., Dordrecht, Holland 1980).
H. Flanders: Differential Forms (Academic Press, New York 1963).
R.K. Dodd, R.K. Bullough: PhysTca Scripta 20, 514 (1979).
V.I. Arnold: Mathematical Methods of Classical Mechanics (Springer-Verlag, Heidelberg 1978) (for example describes Liouville’s theorem).
R.K. Dodd, R.K. Bullough: Proc. Roy. Soc. London A352, 481 (1977).
R.K. Bullough, P.J. Caudrey: in Solitons R.K. Bullough and P.J. Caudrey eds. (Springer-Verlag, Heidelberg 1980) and the other chapters there.
R. Sasaki, R.K. Bullough: Proc. Roy. Soc. London A376, 401 (1981).
H.J. Mikeska: J. Phys. C11, L29 (1978).
L.A. Takhtadzhyan, L.D. Faddeev: Proc. Steklov Inst. of Math Issue 3, 277 (1979).
M. Lakshmanan: Phys. Lett. 61A, 53 (1977).
L.A. Takhtadzhyan: Phys. Lett. 64A, 235 (1977).
M. Lakshmanan, R.K. Bullough: Phys. Lett. 80A, 287 (1980).
C.N. Yang, C.P. Yang: J. Math. Phys. 10, 1115 (1969).
M. Jimbo, T. Miwa, Y. Mori, M. Sato: Physica 1D, 80 (1980).
K. Maki: J. Low Temp. Phys. 41, 327 (1980).
J. Timonen, R.K. Bullough: Phys. Lett. 82A, 183 (1981).
J.K. Kjems, M. Steiner: Phys. Rev. Lett. 41, 1137 (1978).
R.F. Dashen, B. Hasslacher, A. Neveu: Phys. Rev. D11, 3424 (1975).
J. Timonen, A. Luther: “Continuum Limit Correlation Functions for the Spin One Anisotropic Heisenberg Chain”, J. Phys. C. (to appear).
E. Sklyanin: LOMI preprint E-3–1979 (1979).
S. Coleman: Phys. Rev. D11, 2088 (1975).
A.H. Luther: in Solitons ref. [14].
M. Takahashi, M. Suzuki: Prog. Theor. Phys. 48, 2187 (1972).
K. Kakurai, M. Steiner, J.K. Kjems: “Q Dependence of the Soliton Response in CsNiF3 at T=10K and H=5kG” p.141 in Proc. NATO Adv. Stud. Inst. Geilo, Norway (1979) (Plenum 1980).
G. Reiter: Phys. Rev. Lett. 46, 202, 518 (1981).
J.M. Loveluck, T. Schneider, E. Stoll. H.R. Jauslin: Phys. Rev. Lett. 45, 1505 (1980); J. Phys. C: Solid State Phys. 15, 1721 (1982).
V.E. Zakharov, A.B. Shabat: Sov. Phys. JETP 34, 62 (1972).
M.J. Ablowitz, D.J. Kaup, A.C. Newell, H. Segur: Stud. Appl. Maths. LIII, 249 (1974).
L.A. Takhtadzhyan, L.D. Faddeev: Teor. Mat. Fiz. 21, 160 (1974).
R.K. Dodd, R.K. Bullough: in Synergetics A Workshop, H. Haken ed. (Springer-Verlag, Heidelberg 1977).
H. De Vega: Phys. Rev. D22, 2400 (1980).
P.J. Caudrey, J.C. Eilbeck, J.D. Gibbon: Nuovo Cimento 25B, 497 (1975).
J.F. Currie: Phys. Rev. A16, 1692 (1977).
J. Rubinstein: J. Math. Phys. 11, 258 (1970).
V.E. Korepin: Teor. Mat. Fiz. 41, 169 (1979).
E.K. Sklyanin, L.A. Takhtadzhyan, L.D. Faddeev: Teor. Mat. Fiz. 40, 194 (1979).
S.F. Edwards, Y.V. Gulaev: Proc. Roy. Soc. London A279, 229 (1964).
A.M. Arthurs: Proc. Roy. Soc. A313, 445 (1969).
C. Itzykson, J.B. Zuber: Quantum Field Theory (McGraw Hill, New York 1980).
A.G. Izergin, V.E. Korepin: Lett. Math. Phys. 5, 199 (1981).
A.G. Izergin, V.E. Korepin: in Problems in Quantum Field Theory and Statistical Physics, 3 P.P. Kulish and V.N. Popov eds. LOMI Vol 120 “Nauka”, Leningrad. (Also the article by V.O. Tarasov there).
H. Flaschka: Lectures at ELAF ‘84.
D.J. Scalapino, M. Sears, R.S. Ferrell: Phys. Rev. B6, 3409 (1972).
J.A. Krumhansl, J.R. Schrieffer: Phys. Rev. B11, 3535 (1975).
M. Stone, J. Reeve: Phys. Rev. D18, 4746 (1978).
S. Coleman: in The Whys of Sub-Nuclear Physics, A. Zichichi ed. (Plenum, New York, 1977).
S. Goldstein: Proc. Roy. Soc. Edinburgh 49, 210 (1929).
R. Rajaraman, Raj Lakshmi: Phys. Rev. B25, 1866 (1981). 57. M. Lowe, M. Stone: Nucl. Phys. B136, 177 (1978).
H. Flaschka, D.W. McLaughlin: Prog. Theor. Phys. 55, 438 (1976).
H.P. McKean, Jr., P. van Moerbecke: Inventions Math. 30, 217 (1975) and references, B.A. Dubrovin, S.P. Novikov: Zh. Eksp. Teor. Fiz. 67, 2131 (1974) and other references in [58].
H.P. McKean, E. Trubowitz: Comm. Pure. Appl. Math. 29, 143 (1976); Bull. AMS 84, 1042 (1978).
M.G. Forest, D.W. McLaughlin: J. Math. Phys. 23, 1248 (1982).
M.J. Ablowitz, H. Segur: Solitons and the Inverse Scattering Transform (SIAM 1981).
J.F. Currie, J.A. Krumhansl, A.R. Bishop, S.E. Trullinger: Phys. Rev. B22, 477 (1980).
A.R. Bishop, J.A. Krumhansl, S.E. Trullinger: Physica 1D, 1 (1980).
A.R. Bishop: in Physics in One Dimension J. Bernasconi and T. Schneider (Springer-Verlag, Heidelberg 1983).
R.K. Bullough, D.J. Pilling, J. Timonen in Nonlinear Waves L. Debnath ed. (CUP, New York 1983).
R.K. Bullough, D.J. Pilling, J. Timonen: in Proc. 2nd International Workshop in Nonlinear and Turbulent Processes in Physics, Kiev, October 1983. R.Z. Sagdeev, A.V. Gaporov, A.S. Davydov, V.E. Zakharov eds. (Gordon and Breach, New York 1984) in press.
K. Huang: Statistical Physics (J. Wiley and Sons, 1963).
C. Pöppe: Ph.D. Thesis Univ. of Heidelberg, 1980.
H.A. Bethe: Z. Physik 71, 205 (1931).
R.K. Bullough, D.J. Pilling, J. Timonen: “Statistical mechanics of the quantum and classical sine-Gordon fields” in Proc III Intl. Symposium on Selected Topics in Statistical Mechanics. Dubna, August 19841 N.N. Bogolubov Jr. ed. (JINR, Dubna 1984). To appear.
To appear; “Quantum and classical statistical mechanics of the non-linear Schrödinger, sinh-Gordon and sine-Gordon equations” in Proc. 7th Kyoto Summer Institute: Dynamical Problems in Soli ton Systems. S. Takeno ed. Springer Series in Synergetics (Springer-Verlag, Heidelberg, 1984). To appear.
R.J. Baxter: Ann. Phys. 70, 193, 323 (1972).
J.D. Johnson, S. Krinsky, B.M. McCoy: Phys. Rev. A8, 2526 (1973).
P.J. Caudrey: Physica 6D, 126 (1982).
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Bullough, R.K., Pilling, D.J., Timonen, J. (1985). Statistical Mechanics of the sine-Gorden Field: Part II. In: Claro, F. (eds) Nonlinear Phenomena in Physics. Springer Proceedings in Physics, vol 3. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-93289-2_4
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