Journal article

High order Fuchsian equations for the square lattice Ising model: (chi)over-tilde((5))

A Bostan, S Boukraa, AJ Guttmann, S Hassani, I Jensen, J-M Maillard, N Zenine

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | IOP PUBLISHING LTD | Published : 2009

Abstract

We consider the Fuchsian linear differential equation obtained (modulo a prime) for , the five-particle contribution to the susceptibility of the square lattice Ising model. We show that one can understand the factorization of the corresponding linear differential operator from calculations using just a single prime. A particular linear combination of and can be removed from and the resulting series is annihilated by a high order globally nilpotent linear ODE. The corresponding (minimal order) linear differential operator, of order 29, splits into factors of small orders. A fifth-order linear differential operator occurs as the left-most factor of the 'depleted' differential operator and it ..

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