TY - JOUR

T1 - High-order fuchsian equations for the square lattice Ising model

T2 - χ(6)

AU - Boukraa, S.

AU - Hassani, S.

AU - Jensen, I.

AU - Maillard, J. M.

AU - Zenine, N.

PY - 2010/2/26

Y1 - 2010/2/26

N2 - This paper deals with χ(6), the six-particle contribution to the magnetic susceptibility of the square lattice Ising model. We have generated, modulo a prime, series coefficients for χ(6). The length of the series is sufficient to produce the corresponding Fuchsian linear differential equation (modulo a prime). We obtain the Fuchsian linear differential equation that annihilates the depleted series θ(6) = χ(6) - 2/3χ(4) ?+ 2/45 χ(2). The factorization of the corresponding differential operator is performed using a method of factorization modulo a prime, introduced in a previous paper. The depleted differential operator is shown to have a structure similar to the corresponding operator for χ(5). It splits into factors of smaller orders, with the left-most factor of order 6 being equivalent to the symmetric fifth power of the linear differential operator corresponding to the elliptic integral E. The right-most factor has a direct sum structure, and using series calculated modulo several primes, all the factors in the direct sum have been reconstructed in exact arithmetics.

AB - This paper deals with χ(6), the six-particle contribution to the magnetic susceptibility of the square lattice Ising model. We have generated, modulo a prime, series coefficients for χ(6). The length of the series is sufficient to produce the corresponding Fuchsian linear differential equation (modulo a prime). We obtain the Fuchsian linear differential equation that annihilates the depleted series θ(6) = χ(6) - 2/3χ(4) ?+ 2/45 χ(2). The factorization of the corresponding differential operator is performed using a method of factorization modulo a prime, introduced in a previous paper. The depleted differential operator is shown to have a structure similar to the corresponding operator for χ(5). It splits into factors of smaller orders, with the left-most factor of order 6 being equivalent to the symmetric fifth power of the linear differential operator corresponding to the elliptic integral E. The right-most factor has a direct sum structure, and using series calculated modulo several primes, all the factors in the direct sum have been reconstructed in exact arithmetics.

UR - http://www.scopus.com/inward/record.url?scp=77649249430&partnerID=8YFLogxK

UR - http://purl.org/au-research/grants/ARC/DP0770705

U2 - 10.1088/1751-8113/43/11/115201

DO - 10.1088/1751-8113/43/11/115201

M3 - Article

AN - SCOPUS:77649249430

VL - 43

JO - Journal of Physics. A. Mathematical and Theoretical

JF - Journal of Physics. A. Mathematical and Theoretical

SN - 1751-8113

IS - 11

M1 - 115201

ER -