Section: New Results

Computation of integrals related to the Ising model

We showed in [2] that the $n$-fold integrals of the magnetic susceptibility of the Ising model, as well as various other $n$-fold integrals of the “Ising class”, or $n$-fold integrals from enumerative combinatorics, like lattice Green functions, correspond to a distinguished class of functions generalising algebraic functions: they are actually diagonals of rational functions. This algebraic structure explains many remarkable properties of the integrals of the Ising class.