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Square lattice Ising model susceptibility: connection matrices and singular behaviour of ${\chi }^{\left(3\right)}$ and ${\chi }^{\left(4\right)}$. (English) Zbl 1087.82006
In the paper a simple and efficient method to calculate numerically, with an arbitrary number of digits, the connection matrices between the independent solutions, defined at two singular points, of differential equations of quite high orders is introduced. The order 7 and 10 Fuchsian ODEs corresponding to the 3-and 4-particle contribution to the magnetic susceptibility of the Ising model is considered. The entries of the connection matrix between two regular singular points have been obtained in the floating point form and most of them have been recognized, particularly those that show up in the singular behaviour of the physical solutions.
##### MSC:
 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs 34M55 Painlevé and other special equations; classification, hierarchies 32G34 Moduli and deformations for ordinary differential equations 82B27 Critical phenomena (equilibrium statistical mechanics)
##### Keywords:
Ising model; connection matrices; singular behaviour