The Fuchsian differential equation of the square lattice Ising model $\chi (3)$ susceptibility

Abstract

Using an expansion method in the variables $x_i$ that appear in the $(n-1)$-dimensional integrals representing the $n$-particle contribution to the Ising square lattice model susceptibility $\chi$, we generate a long series of coefficients for the 3-particle contribution ${\chi }^{(3)}$, using a $N^4$ polynomial time algorithm. We give the Fuchsian differential equation of order seven for ${\chi }^{(3)}$ that reproduces all the terms of our long series. An analysis of the properties of this Fuchsian differential equation is performed.

15 pages, no figures, submitted to J. Phys. A