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Zbl 1086.82520
Zenine, N.; Boukraa, S.; Hassani, S.; Maillard, J.-M.
Ising model susceptibility: the Fuchsian differential equation for $\chi^{(4)}$ and its factorization properties.
(English)
[J] J. Phys. A, Math. Gen. 38, No. 19, 4149-4173 (2005). ISSN 0305-4470

Summary: We give the Fuchsian linear differential equation satisfied by $\chi^{(4)}$, the 'four-particle' contribution to the susceptibility of the isotropic square lattice Ising model. This Fuchsian differential equation is deduced from a series expansion method introduced in two previous papers and is applied with some symmetries and tricks specific to $\chi^{(4)}$. The corresponding order ten linear differential operator exhibits a large set of factorization properties. Among these factorizations one is highly remarkable: it corresponds to the fact that the two-particle contribution $\chi^{(2)}$ is actually a solution of this order ten linear differential operator. This result, together with a similar one for the order seven differential operator corresponding to the three-particle contribution, $\chi^{(3)}$, leads us to a conjecture on the structure of all the n-particle contributions $\chi^{(n)}$.
MSC 2000:
*82B20 Lattice systems
34M55 Painlevé and other special equations
47E05 Ordinary differential operators
81Q05 Closed and approximate solutions to quantum-mechanical equations
32G34 Moduli and deformations for ODE

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