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We give the Fuchsian linear differential equation satisfied by $\chi^{(4)}$,the ``four-particle'' contribution to the susceptibility of the isotropicsquare lattice Ising model. This Fuchsian differential equation is deduced froma series expansion method introduced in two previous papers and is applied withsome symmetries and tricks specific to $\chi^{(4)}$. The corresponding orderten linear differential operator exhibits a large set of factorizationproperties. Among these factorizations one is highly remarkable: it correspondsto the fact that the two-particle contribution $\chi^{(2)}$ is actually asolution of this order ten linear differential operator. This result, togetherwith a similar one for the order seven differential operator corresponding tothe three-particle contribution, $\chi^{(3)}$, leads us to a conjecture on thestructure of all the $ n$-particle contributions $ \chi^{(n)}$.Comment: 27 pages no figure

Ising model susceptibility: the Fuchsian differential equation for χ(4)and its factorization properties

Ising model susceptibility: the Fuchsian differential equation for χ⁽⁴⁾and its factorization properties