Home Search Collections Journals About Contact us My IOPscience The Ising model: from elliptic curves to modular forms and Calabi–Yau equations This content has been downloaded from IOPscience. Please scroll down to see the full text. 2011 J. Phys. A: Math. Theor. 44 045204 (http://iopscience.iop.org/1751-8121/44/4/045204) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 134.157.8.77 This content was downloaded on 11/03/2015 at 12:38 Please note that terms and conditions apply. IOP PUBLISHING JOURNAL OF PHYSICS A: MATHEMATICAL AND THEORETICAL J. Phys. A: Math. Theor. 44 (2011) 045204 (44pp) doi:10.1088/1751-8113/44/4/045204 The Ising model: from elliptic curves to modular forms and Calabi–Yau equations ABostan1, S Boukraa2,7, S Hassani3,7, M van Hoeij4,7, J-M Maillard5, J-A Weil6 and N Zenine3 1 INRIA Paris-Rocquencourt, Domaine de Voluceau, B.P. 105 78153 Le Chesnay Cedex, France 2 LPTHIRM and Departement´ d’Aeronautique,´ Universite´ de Blida, Blida, Algeria 3 Centre de Recherche Nucleaire´ d’Alger, 2 Bd. Frantz Fanon, BP 399, 16000 Alger, Algeria 4 Florida State University, Department of Mathematics, 1017 Academic Way, Tallahassee, FL 32306-4510, USA 5 LPTMC, UMR 7600 CNRS, Universite´ de Paris, Tour 23, 5eme` etage,´ Case 121, 4 Place Jussieu, 75252 Paris Cedex 05, France 6 XLIM, Universite´ de Limoges, 123 Avenue Albert Thomas, 87060 Limoges Cedex, France E-mail:
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[email protected] Received 4 July 2010, in final form 24 November 2010 Published 6 January 2011 Online at stacks.iop.org/JPhysA/44/045204 Abstract We show that almost all the linear differential operators factors obtained in the analysis of the n-particle contributionsχ ˜ (n)’s of the susceptibility of the Ising model for n 6 are linear differential operators associated with elliptic curves.