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The Fuchsian differential equation of the square lattice Ising model χ (3) susceptibility. (English) Zbl 1073.82014

Summary: Using an expansion method in the variables x i that appear in (n-1)-dimensional integrals representing the n-particle contribution to the Ising square lattice model susceptibility χ, we generate a long series of coefficients for the three-particle contribution χ (3) , using an N 4 polynomial time algorithm. We give the Fuchsian differential equation of order 7 for χ (3) that reproduces all the terms of our long series. An analysis of the properties of this Fuchsian differential equation is performed.

For additional information see [B. G. Nickel, ibid. 38, No. 20, 4517–4518 (2005; Zbl 1074.82010).

82B27Critical phenomena (equilibrium statistical mechanics)
34M55Painlevé and other special equations; classification, hierarchies
82B20Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs