S. Boukraa

The Fuchsian differential equation of the square lattice Ising model χ (3) susceptibility

Using an expansion method in the variables xi that appear in (n ? 1)-dimensional integrals representing the n-particle contribution to the Ising square lattice model susceptibility ?, we generate a long series of coefficients for the three-particle contribution ?(3), using an N4 polynomial time algorithm. We give the Fuchsian differential equation of order 7 for ?(3) that reproduces all the terms of our long series. An analysis of the properties of this Fuchsian differential equation is performed.

High order Fuchsian equations for the square lattice Ising model: \tilde{\chi}^{(5)}

We consider the Fuchsian linear differential equation obtained (modulo a prime) for

Square lattice Ising model susceptibility: connection matrices and singular behaviour of χ (3) and χ (4)

tilde{chi}^{(5)}

The diagonal Ising susceptibility

, 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

Ising model susceptibility: the Fuchsian differential equation for χ(4) and its factorization properties

tilde{chi}^{(1)}

Square lattice Ising model susceptibility: series expansion method and differential equation for χ(3)

and

Growth-complexity spectrum of some discrete dynamical systems

tilde{chi}^{(3)}

Factorization properties of birational mappings

can be removed from

Singularities of n-fold integrals of the Ising class and the theory of elliptic curves

tilde{chi}^{(5)}

Integrable mappings and polynomial growth

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 is shown to be equivalent to the symmetric fourth power of