### Abstract

This paper deals with χ(6), the six-particle contribution to the magnetic susceptibility of the square lattice Ising model. We have generated, modulo a prime, series coefficients for χ(6). The length of the series is sufficient to produce the corresponding Fuchsian linear differential equation (modulo a prime). We obtain the Fuchsian linear differential equation that annihilates the depleted series θ(6) = χ(6) - 2/3χ(4) ?+ 2/45 χ(2). The factorization of the corresponding differential operator is performed using a method of factorization modulo a prime, introduced in a previous paper. The depleted differential operator is shown to have a structure similar to the corresponding operator for χ(5). It splits into factors of smaller orders, with the left-most factor of order 6 being equivalent to the symmetric fifth power of the linear differential operator corresponding to the elliptic integral E. The right-most factor has a direct sum structure, and using series calculated modulo several primes, all the factors in the direct sum have been reconstructed in exact arithmetics.

Original language | English |
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Article number | 115201 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 43 |

Issue number | 11 |

DOIs | |

Publication status | Published - 26 Feb 2010 |

Externally published | Yes |

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## Cite this

Boukraa, S., Hassani, S., Jensen, I., Maillard, J. M., & Zenine, N. (2010). High-order fuchsian equations for the square lattice Ising model: χ

^{(6)}.*Journal of Physics A: Mathematical and Theoretical*,*43*(11), [115201]. https://doi.org/10.1088/1751-8113/43/11/115201, https://doi.org/10.1088/1751-8113/43/11/115201