Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1086.82520
Zenine, N.; Boukraa, S.; Hassani, S.; Maillard, J.-M.
Ising model susceptibility: the Fuchsian differential equation for $\chi^{(4)}$ and its factorization properties. (English)
[J] J. Phys. A, Math. Gen. 38, No. 19, 4149-4173 (2005). ISSN 0305-4470

Summary: We give the Fuchsian linear differential equation satisfied by $\chi^{(4)}$, the 'four-particle' contribution to the susceptibility of the isotropic square lattice Ising model. This Fuchsian differential equation is deduced from a series expansion method introduced in two previous papers and is applied with some symmetries and tricks specific to $\chi^{(4)}$. The corresponding order ten linear differential operator exhibits a large set of factorization properties. Among these factorizations one is highly remarkable: it corresponds to the fact that the two-particle contribution $\chi^{(2)}$ is actually a solution of this order ten linear differential operator. This result, together with a similar one for the order seven differential operator corresponding to the three-particle contribution, $\chi^{(3)}$, leads us to a conjecture on the structure of all the n-particle contributions $\chi^{(n)}$.

MSC 2000:: *82B20 Lattice systems
34M55 Painlevé and other special equations
47E05 Ordinary differential operators
81Q05 Closed and approximate solutions to quantum-mechanical equations
32G34 Moduli and deformations for ODE

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]