# The Ising model and special geometries

@article{Boukraa2014TheIM, title={The Ising model and special geometries}, author={Salah Boukraa and Saoud Hassani and J-M Maillard}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2014}, volume={47} }

We show that the globally nilpotent G-operators corresponding to the factors of the linear differential operators annihilating the multifold integrals χ(n) of the magnetic susceptibility of the Ising model (n ⩽ 6) are homomorphic to their adjoint. This property of being self-adjoint up to operator homomorphisms is equivalent to the feature of their symmetric squares, or their exterior squares, having rational solutions. The differential Galois groups are in the special orthogonal, or symplectic…

## 8 Citations

Canonical decomposition of irreducible linear differential operators with symplectic or orthogonal differential Galois groups

- Mathematics
- 2015

We first revisit an order-six linear differential operator, already introduced in a previous paper, having a solution which is a diagonal of a rational function of three variables. This linear…

Selected non-holonomic functions in lattice statistical mechanics and enumerative combinatorics

- Mathematics
- 2015

We recall that the full susceptibility series of the Ising model, modulo powers of the prime 2 ?> , reduce to algebraic functions. We also recall the nonlinear polynomial differential equation…

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- Mathematics
- 2015

We recall that diagonals of rational functions naturally occur in lattice statistical mechanics and enumerative combinatorics. In all the examples emerging from physics, the minimal linear…

Lattice Green functions: the seven-dimensional face-centred cubic lattice

- Mathematics
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We present a recursive method to generate the expansion of the lattice Green function of the d-dimensional face-centred cubic (fcc) lattice. We produce a long series for d = 7. Then we show (and…

Automata and the susceptibility of the square lattice Ising model modulo powers of primes

- Mathematics, Computer Science
- 2015

Underline the importance of studying a new class of functions corresponding to ratios of diagonals of rational functions: they reduce to algebraic functions modulo powers of primes and they may have solutions with natural boundaries.

Scaling functions in the square Ising model

- Mathematics
- 2014

We show and give the linear differential operators q scal ?> of order q = n 2 / 4 + n + 7 / 8 + ( − 1 ) n / 8 ?> , for the integrals I n ( r ) ?> which appear in the two-point correlation scaling…

Lattice Green functions: the d-dimensional face-centered cubic lattice, d = 8, 9, 10, 11, 12

- Mathematics
- 2016

We previously reported on a recursive method to generate the expansion of the lattice Green function (LGF) of the d-dimensional face-centered cubic lattice (fcc). The method was used to generate many…

Integrability and non-integrability in the Ising model

- Physics
- 2014

of the Dissertation Integrability and non-integrability in the Ising model

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