The diagonal Ising susceptibility
Identifieur interne : 000174 ( France/Analysis ); précédent : 000173; suivant : 000175The diagonal Ising susceptibility
Auteurs : S. Boukraa [Algérie] ; S. Hassani [Algérie] ; J-M Maillard [France] ; B M Mccoy [États-Unis] ; N. Zenine [Algérie]Source :
- Journal of Physics A: Mathematical and Theoretical [ 1751-8113 ] ; 2007.
Abstract
We use the recently derived form factor expansions of the diagonal two-point correlation function of the square Ising model to study the susceptibility for a magnetic field applied only to one diagonal of the square lattice, for the isotropic Ising model. We exactly evaluate the one and two particle contributions (1)d and (2)d of the corresponding susceptibility, and obtain linear differential equations for the three and four particle contributions, as well as the five particle contribution (5)d, but only modulo a given prime. We use these exact linear differential equations to show that not only the Russian-doll structure but also the direct sum structure on the linear differential operators for the n-particle contributions (n)d are quite directly inherited from the direct sum structure on the form factors f(n). We show that the nth particle contributions (n)d have their singularities at roots of unity. These singularities become dense on the unit circle sinh2Ev/kTsinh2Eh/kT 1 as n .
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DOI: 10.1088/1751-8113/40/29/002
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We exactly evaluate the one and two particle contributions (1)d and (2)d of the corresponding susceptibility, and obtain linear differential equations for the three and four particle contributions, as well as the five particle contribution (5)d, but only modulo a given prime. We use these exact linear differential equations to show that not only the Russian-doll structure but also the direct sum structure on the linear differential operators for the n-particle contributions (n)d are quite directly inherited from the direct sum structure on the form factors f(n). We show that the nth particle contributions (n)d have their singularities at roots of unity. These singularities become dense on the unit circle sinh2Ev/kTsinh2Eh/kT 1 as n .</div></front></TEI><affiliations><list><country><li>Algérie</li><li>France</li><li>États-Unis</li></country><region><li>Wilaya d'Alger</li><li>Île-de-France</li></region><settlement><li>Alger</li><li>Paris</li></settlement></list><tree><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="France"><region name="Île-de-France"><name sortKey="Maillard, J M" sort="Maillard, J M" uniqKey="Maillard J" first="J-M" last="Maillard">J-M Maillard</name></region><name sortKey="Maillard, J M" sort="Maillard, J M" uniqKey="Maillard J" first="J-M" last="Maillard">J-M Maillard</name></country><country name="États-Unis"><noRegion><name sortKey="Mccoy, B M" sort="Mccoy, B M" uniqKey="Mccoy B" first="B M" last="Mccoy">B M Mccoy</name></noRegion><name sortKey="Mccoy, B M" sort="Mccoy, B M" uniqKey="Mccoy B" first="B M" last="Mccoy">B M Mccoy</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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