High order Fuchsian equations for the square lattice Ising model:
Identifieur interne : 000131 ( France/Analysis ); précédent : 000130; suivant : 000132High order Fuchsian equations for the square lattice Ising model:
Auteurs : A. Bostan [France] ; S. Boukraa [Algérie] ; A J Guttmann [Australie] ; S. Hassani [Algérie, Australie] ; I. Jensen [Australie, France] ; J-M Maillard [France] ; N. Zenine [Algérie]Source :
- Journal of Physics A: Mathematical and Theoretical [ 1751-8113 ] ; 2009.
Abstract
We consider the Fuchsian linear differential equation obtained (modulo a prime) for , the five-particle contribution to the susceptibility of the square lattice Ising model. We show that one can understand the factorization of the corresponding linear differential operator from calculations using just a single prime. A particular linear combination of and can be removed from and the resulting series is annihilated by a high order globally nilpotent linear ODE. The corresponding (minimal order) linear differential operator, of order 29, splits into factors of small orders. A fifth-order linear differential operator occurs as the left-most factor of the depleted differential operator and it is shown to be equivalent to the symmetric fourth power of LE, the linear differential operator corresponding to the elliptic integral E. This result generalizes what we have found for the lower order terms and . We conjecture that a linear differential operator equivalent to a symmetric (n 1) th power of LE occurs as a left-most factor in the minimal order linear differential operators for all 's.
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DOI: 10.1088/1751-8113/42/27/275209
Affiliations:
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Jensen</name><name sortKey="Maillard, J M" sort="Maillard, J M" uniqKey="Maillard J" first="J-M" last="Maillard">J-M Maillard</name><name sortKey="Maillard, J M" sort="Maillard, J M" uniqKey="Maillard J" first="J-M" last="Maillard">J-M Maillard</name></country><country name="Algérie"><noRegion><name sortKey="Boukraa, S" sort="Boukraa, S" uniqKey="Boukraa S" first="S" last="Boukraa">S. Boukraa</name></noRegion><name sortKey="Boukraa, S" sort="Boukraa, S" uniqKey="Boukraa S" first="S" last="Boukraa">S. Boukraa</name><name sortKey="Hassani, S" sort="Hassani, S" uniqKey="Hassani S" first="S" last="Hassani">S. Hassani</name><name sortKey="Zenine, N" sort="Zenine, N" uniqKey="Zenine N" first="N" last="Zenine">N. Zenine</name></country><country name="Australie"><noRegion><name sortKey="Guttmann, A J" sort="Guttmann, A J" uniqKey="Guttmann A" first="A J" last="Guttmann">A J Guttmann</name></noRegion><name sortKey="Guttmann, A J" sort="Guttmann, A J" uniqKey="Guttmann A" first="A J" last="Guttmann">A J Guttmann</name><name sortKey="Hassani, S" sort="Hassani, S" uniqKey="Hassani S" first="S" last="Hassani">S. Hassani</name><name sortKey="Jensen, I" sort="Jensen, I" uniqKey="Jensen I" first="I" last="Jensen">I. Jensen</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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