Free field construction for correlation functions of the eight-vertex model |
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| Institution: | 1. Wigner Research Centre for Physics, Konkoly-Thege Miklós u. 29-33, 1121 Budapest, Hungary;2. Roland Eötvös University, Pázmány Péter sétány 1/A, 1117 Budapest, Hungary;1. Indiana University, Department of Mathematics, Bloomington, IN 47401, USA;2. Universität Wien, Fakultät für Mathematik, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria;1. Faculty of Pharmaceutical Sciences, Tokushima Bunri University, Tokushima 770-8514, Japan;2. Kitasato Institute for Life Sciences, Kitasato University, 5-9-1 Shirokane, Minato Ward, Tokyo 108-8641, Japan;1. Saha Institute of Nuclear Physics, HBNI, 1/AF Bidhannagar, Kolkata-700064, India;2. Department of Physics, Banaras Hindu University, Varanasi-221005, India;3. Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata-700108, India;1. Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, D14476 Potsdam, Germany;2. Institut für Physik und IRIS Adlershof, Humboldt-Universität zu Berlin, Zum Grossen Windkanal 6, D12489 Berlin, Germany;3. Institute of Radiation Problems ANAS, B.Vahabzade 9, AZ1143 Baku, Azerbaijan;4. Department of Mathematics, Khazar University, Mehseti St. 41, AZ1096, Baku, Azerbaijan;5. Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, SE-412 96 Göteborg, Sweden;1. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1;2. 215 Carnegie Building, Department of Mathematics, Syracuse University, Syracuse, NY 13244, USA |
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| Abstract: | A free field representation for the type I vertex operators and the corner transfer matrices of the eight-vertex model is proposed. The construction uses the vertex-face correspondence, which makes it possible to express correlation functions of the eight-vertex model in terms of correlation functions of the SOS model with a non-local insertion. This new non-local insertion admits a free field representation in terms of Lukyanov's screening operator. The spectrum of the corner transfer matrix and the Baxter-Kelland formula for the average staggered polarization have been reproduced. |
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