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

Details The Fuchsian differential equation of the square lattice Ising model $χ(3)$ susceptibility The Fuchsian differential equation of the square lattice Ising model $χ(3)$ susceptibility

2004-07-26

arxiv.org/abs/math-ph/0407060v1

J.Phys. A37 (2004) 9651-9668

Physics

Mathematical Physics

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

Scientific paper

10.1088/0305-4470/37/41/004

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.

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