The Ising model: from elliptic curves to modular forms and Calabi–Yau equations

@article{Bostan2010TheIM,
  title={The Ising model: from elliptic curves to modular forms and Calabi–Yau equations},
  author={Alin Bostan and Salah Boukraa and Saoud Hassani and Mark van Hoeij and J-M Maillard and Jacques-Arthur Weil and Nadjah Zenine},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2010},
  volume={44},
  pages={045204}
}
We show that almost all the linear differential operators factors obtained in the analysis of the n-particle contributions 's of the susceptibility of the Ising model for n ⩽ 6 are linear differential operators associated with elliptic curves. Beyond the simplest differential operators factors which are homomorphic to symmetric powers of the second order operator associated with the complete elliptic integral E, the second and third order differential operators Z2, F2, F3, can actually be… 

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