Advanced Search

Query:

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

Format:

Display: entries per page entries

Zbl 1113.82020
Zenine, N.; Boukraa, S.; Hassani, S.; Maillard, J.-M.
Square lattice Ising model susceptibility: series expansion method and differential equation for $\chi^{(3)}$. (English)
[J] J. Phys. A, Math. Gen. 38, No. 9, 1875-1899 (2005). ISSN 0305-4470

Summary: In a previous paper [J. Phys. A 37, No. 41, 9651--9668 (2004; Zbl 1073.82014)] we gave the Fuchsian linear differential equation satisfied by $\chi^{(3)}$, the `three-particle' contribution to the susceptibility of the isotropic square lattice Ising model. This paper gives the details of the calculations (with some useful tricks and tools) which allow one to obtain a long series in polynomial time. The method is based on series expansion in the variables that appear in the $(n-1)$-dimensional integrals representing the $n$-particle contribution to the isotropic square lattice Ising model susceptibility $\chi$. The integration rules are straightforward due to remarkable formulae we derive for these variables. We obtain without any numerical approximation $\chi^{(3)}$ as a fully integrated series in the variable $w=s/2/(1+s^2)$, where $s=\sinh(2K)$, with $K=J/kT$ the conventional Ising model coupling constant. We also give some perspectives and comments on these results.

MSC 2000:: *82B27 Critical phenomena
34M55 Painlevé and other special equations
82B10 Quantum equilibrium statistical mechanics (general)

Citations: Zbl 1073.82014

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]