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Zbl 1073.82014
Zenine, N.; Boukraa, S.; Hassani, S.; Maillard, J.-M.
The Fuchsian differential equation of the square lattice Ising model $\chi^{(3)}$ susceptibility. (English)
[J] J. Phys. A, Math. Gen. 37, No. 41, 9651-9668 (2004). ISSN 0305-4470

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 $\chi$, we generate a long series of coefficients for the three-particle contribution $\chi^{(3)}$, using an $N^4$ polynomial time algorithm. We give the Fuchsian differential equation of order 7 for $\chi^{(3)}$ 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 [{\it B. G. Nickel}, ibid. 38, No. 20, 4517--4518 (2005; Zbl 1074.82010).

MSC 2000:: *82B27 Critical phenomena
34M55 Painlevé and other special equations
82B20 Lattice systems

Citations: Zbl 1074.82010

Cited in: Zbl 1113.82020 Zbl 1074.82010

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Zentralblatt MATH Berlin [Germany]