Using an expansion method in the variables $x_i$ that appear in the $(n-1)$-dimensional integrals representing the $n$-particle contribution to the Ising square lattice model susceptibility $\chi$, we generate a long series of coefficients for the 3-particle contribution $\chi^{(3)}$, using a $N^4$ polynomial time algorithm. We give the Fuchsian differential equation of order seven for $\chi^{(3)}$ that reproduces all the terms of our long series. An analysis of the properties of this Fuchsian differential equation is performed.
Publié le : 2004-07-05
Classification:
rigid local systems.,
rigid local systems,
indicial equations,
apparent singularities,
holonomy theory,
Fuchsian differential equations,
series expansions,
Susceptibility of the Ising model,
05.50.+q, 05.10.-a, 02.30.Hq, 02.30.Gp, 02.40.Xx, 34M55, 47E05, 81Qxx, 32G34, 34Lxx, 34Mxx, 14Kxx,
[PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech],
[MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG],
[NLIN.NLIN-SI]Nonlinear Sciences [physics]/Exactly Solvable and Integrable Systems [nlin.SI],
[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph]
@article{hal-00002775,
author = {Zenine, N. and Boukraa, S. and Hassani, S. and Maillard, J.-M.},
title = {The Fuchsian differential equation of the square lattice Ising model Ki(3) susceptibility},
journal = {HAL},
volume = {2004},
number = {0},
year = {2004},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00002775}
}
Zenine, N.; Boukraa, S.; Hassani, S.; Maillard, J.-M. The Fuchsian differential equation of the square lattice Ising model Ki(3) susceptibility. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00002775/