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Ising model susceptibility: Fuchsian differential equation for $χ^{(4)}$ and its factorization properties

N. Zenine·S. Boukraa·S. Hassani·J. -M. Maillard
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Abstract

We give the Fuchsian linear differential equation satisfied by $χ^{(4)}$, 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 $χ^{(4)}$. 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 $χ^{(2)}$ 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, $χ^{(3)}$, leads us to a conjecture on the structure of all the $ n$-particle contributions $ χ^{(n)}$.

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N. Zenine, S. Boukraa, S. Hassani, J. -M. Maillard. 2005-02-07. Ising model susceptibility: Fuchsian differential equation for $χ^{(4)}$ and its factorization properties. https://doi.org/10.1088/0305-4470%2F38%2F19%2F007

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