@article{BBHMWZ09,
    author      = {A. Bostan and S. Boukraa and S. Hassani and J. -M. Maillard
  and J. -A. Weil and N. Zenine},
    title       = {Globally nilpotent differential operators and the square
  {I}sing model},
    journal     = {J. Phys. A: Math. Theor.},
    number      = {12},
    year        = {2009},
    volume      = {42},
    pages       = {50pp},
    doi         = {10.1088/1751-8113/42/12/125206},
    abstract    = {We recall various multiple integrals related to the
  isotropic square Ising model, and corresponding, respectively, to the
  n-particle contributions of the magnetic susceptibility, to the (lattice)
  form factors, to the two-point correlation functions and to their
  lambda-extensions. These integrals are holonomic and even G-functions: they
  satisfy Fuchsian linear differential equations with polynomial coefficients
  and have some arithmetic properties. We recall the explicit forms, found in
  previous work, of these Fuchsian equations. These differential operators are
  very selected Fuchsian linear differential operators, and their remarkable
  properties have a deep geometrical origin: they are all globally nilpotent,
  or, sometimes, even have zero p-curvature. Focusing on the factorised parts
  of all these operators, we find out that the global nilpotence of the factors
  corresponds to a set of selected structures of algebraic geometry: elliptic
  curves, modular curves, and even a remarkable weight-1 modular form emerging
  in the three-particle contribution $\chi^{(3)}$ of the magnetic
  susceptibility of the square Ising model. In the case where we do not have
  G-functions, but Hamburger functions (one irregular singularity at 0 or
  $\infty$) that correspond to the confluence of singularities in the scaling
  limit, the p-curvature is also found to verify new structures associated with
  simple deformations of the nilpotent property.},
}