Square lattice Ising model (chi)over-tilde((5)) ODE in exact arithmetic
B Nickel, I Jensen, S Boukraa, AJ Guttmann, S Hassani, J-M Maillard, N Zenine
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | IOP PUBLISHING LTD | Published : 2010
We obtain in exact arithmetic the order 24 linear differential operator L24 and the right-hand side E(5) of the inhomogeneous equation L24(Φ(5)) = E(5), where φ(5) = χ̃(5) - χ̃(3)/2 + χ̃(1)/120 is a linear combination of n-particle contributions to the susceptibility of the square lattice Ising model. In Bostan et al (2009 J. Phys. A: Math. Theor. 42 275209), the operator L24 (modulo a prime) was shown to factorize into L(left)12 · L(right)12; here we prove that no further factorization of the order 12 operator L(left)12 is possible. We use the exact ODE to obtain the behaviour of χ̃ (5) at the ferromagnetic critical point and to obtain a limited number of analytic continuations of χ̃(5) bey..View full abstract
IJ and AJG are supported by the Australian Research Council. The calculations would not have been possible without a generous grant from the National Computational Infrastructure (NCI) whose National Facility provides the national peak computing facility for Australian researchers. This work has been performed without any support from the ANR, the ERC and the MAE.