By Helen Au-Yang, Jacques H. H. Perk (auth.), Masaki Kashiwara, Tetsuji Miwa (eds.)

Developments in mathematical physics through the moment half the 20 th century prompted a few mathematical components, one of the extra major being illustration conception, differential equations, combinatorics, and algebraic geometry. In them all, the dynamic position of integrable versions has been imperative, principally because of crucial houses: the truth that integrable types own countless levels of freedom and limitless dimensional symmetries. This quantity makes a speciality of the continued value of integrability in masking the next subject matters: conformal box thought, monstrous quantum box conception, solvable lattice versions, quantum affine algebras, the Painlevé equations and combinatorics.

Contributors: H. Au-Yang, R.J. Baxter, H.E. Boos, E. Date, okay. Fabricius, V.A. Fateev, B. Feigin, G.Hatayama, A. Its, M. Jimbo, A. Kapaev, A.N. Kirillov, V.E. Korepin, A.Kuniba, J.M. Maillet, B.M. McCoy, C. Mercat, T. Miwa, A. Nakayashiki, M.Okado, C.H.Otto Chui, P.A. Pearce, J.H.H. Perk, V. Petkova, A. Schilling, F.A. Smirnov, T.Takagi, Y. Takeyama, M. Taneda, C.A. Tracy, Z.Tsuboi, H. Widom, J.-B. Zuber 'MathPhys

"Odyssey 2001" will function an exceptional reference textual content for mathematical physicists and graduate scholars in a few areas.

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Extra info for MathPhys Odyssey 2001: Integrable Models and Beyond In Honor of Barry M. McCoy

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We evaluate I for the Ising, self-dual Potts, self-dual Ashkin-Teller, KashiwaraMiwa, chiral Potts and Fateev-Zamolodchikov models. In all cases it is either one, or is related to the modulus k (or k'). AMS subject classification: Primary 82B20; secondary 82B23. Keywords and phrases: statistical mechanics; lattice models; star-triangle relation; exactly solvable models; Kashiwara-Miwa model; chiral Potts model. M. Kashiwara et al. J. Baxter Star-triangle Relation Consider a model on the square lattice where spins take values 0, ...

H. H. Perk and H. W. Capel, Time-Dependent xx-Correlations in the OneDimensional XY-Model, PhysicaA 89 (1977) 265-303. [42] B. M. McCoy and T. T. Wu, Nonlinear Partial Difference Equationsfor the TwoDimensional Ising Model, Phys. Rev. Lett. 45 (1980) 675-678. [43] 1. H. H. Perk, Equations of Motion for the Transverse Correlations of the OneDimensional XY-Model at Finite Temperature, Phys. Lett. A 79 (1980) 1-2. [44] J. H. H. Perk, Quadratic Identities for Ising Model Correlations, Phys. Lett. A 79 (1980) 3-5.

W. Capel, Time-Dependent xx-Correlations in the OneDimensional XY-Model, PhysicaA 89 (1977) 265-303. [42] B. M. McCoy and T. T. Wu, Nonlinear Partial Difference Equationsfor the TwoDimensional Ising Model, Phys. Rev. Lett. 45 (1980) 675-678. [43] 1. H. H. Perk, Equations of Motion for the Transverse Correlations of the OneDimensional XY-Model at Finite Temperature, Phys. Lett. A 79 (1980) 1-2. [44] J. H. H. Perk, Quadratic Identities for Ising Model Correlations, Phys. Lett. A 79 (1980) 3-5. [45] B.

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