Landau singularities and singularities of holonomic integrals of the Ising class
Identifieur interne : 000177 ( France/Analysis ); précédent : 000176; suivant : 000178Landau singularities and singularities of holonomic integrals of the Ising class
Auteurs : S. Boukraa [Algérie] ; S. Hassani [Algérie] ; J-M Maillard [France] ; N. Zenine [Algérie]Source :
- Journal of Physics A: Mathematical and Theoretical [ 1751-8113 ] ; 2007.
Abstract
We consider families of multiple and simple integrals of the Ising class and the linear ordinary differential equations with polynomial coefficients they are solutions of. We compare the full set of singularities given by the roots of the head polynomial of these linear ODEs and the subset of singularities occurring in the integrals, with the singularities obtained from the Landau conditions. For these Ising class integrals, we show that the Landau conditions can be worked out, either to give the singularities of the corresponding linear differential equation or the singularities occurring in the integral. The singular behaviour of these integrals is obtained in the self-dual variable w s/2/(1 s2), with s sinh(2K), where K J/kT is the usual Ising model coupling constant. Switching to the variable s, we show that the singularities of the analytic continuation of series expansions of these integrals actually break the KramersWannier duality. We revisit the singular behaviour (Zenine et al 2005 J. Phys. A: Math. Gen. 38 943974) of the third contribution to the magnetic susceptibility of Ising model (3) at the points 1 3w 4w2 0 and show that (3)(s) is not singular at the corresponding points inside the unit circle s 1, while its analytical continuation in the variable s is actually singular at the corresponding points 2 s s2 0 outside the unit circle (s > 1).
Url:
DOI: 10.1088/1751-8113/40/11/001
Affiliations:
Links toward previous steps (curation, corpus...)
- to stream Istex, to step Corpus: 001724
- to stream Istex, to step Curation: 001187
- to stream Istex, to step Checkpoint: 000245
- to stream Main, to step Merge: 000640
- to stream Main, to step Curation: 000622
- to stream Main, to step Exploration: 000622
- to stream France, to step Extraction: 000177
Links to Exploration step
ISTEX:FF92A8B1E5A2C986F1E81D4B6C340ACA549EC532Le document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">Landau singularities and singularities of holonomic integrals of the Ising class</title>
<author><name sortKey="Boukraa, S" sort="Boukraa, S" uniqKey="Boukraa S" first="S" last="Boukraa">S. Boukraa</name>
</author>
<author><name sortKey="Hassani, S" sort="Hassani, S" uniqKey="Hassani S" first="S" last="Hassani">S. Hassani</name>
</author>
<author><name sortKey="Maillard, J M" sort="Maillard, J M" uniqKey="Maillard J" first="J-M" last="Maillard">J-M Maillard</name>
</author>
<author><name sortKey="Zenine, N" sort="Zenine, N" uniqKey="Zenine N" first="N" last="Zenine">N. Zenine</name>
</author>
</titleStmt>
<publicationStmt><idno type="wicri:source">ISTEX</idno>
<idno type="RBID">ISTEX:FF92A8B1E5A2C986F1E81D4B6C340ACA549EC532</idno>
<date when="2007" year="2007">2007</date>
<idno type="doi">10.1088/1751-8113/40/11/001</idno>
<idno type="url">https://api.istex.fr/document/FF92A8B1E5A2C986F1E81D4B6C340ACA549EC532/fulltext/pdf</idno>
<idno type="wicri:Area/Istex/Corpus">001724</idno>
<idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">001724</idno>
<idno type="wicri:Area/Istex/Curation">001187</idno>
<idno type="wicri:Area/Istex/Checkpoint">000245</idno>
<idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Checkpoint">000245</idno>
<idno type="wicri:doubleKey">1751-8113:2007:Boukraa S:landau:singularities:and</idno>
<idno type="wicri:Area/Main/Merge">000640</idno>
<idno type="wicri:Area/Main/Curation">000622</idno>
<idno type="wicri:Area/Main/Exploration">000622</idno>
<idno type="wicri:Area/France/Extraction">000177</idno>
</publicationStmt>
<sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">Landau singularities and singularities of holonomic integrals of the Ising class</title>
<author><name sortKey="Boukraa, S" sort="Boukraa, S" uniqKey="Boukraa S" first="S" last="Boukraa">S. Boukraa</name>
<affiliation wicri:level="1"><country xml:lang="fr">Algérie</country>
<wicri:regionArea>LPTHIRM and Dpartement d'Aronautique, Universit de Blida, Blida</wicri:regionArea>
<wicri:noRegion>Blida</wicri:noRegion>
</affiliation>
<affiliation wicri:level="1"><country wicri:rule="url">Algérie</country>
</affiliation>
</author>
<author><name sortKey="Hassani, S" sort="Hassani, S" uniqKey="Hassani S" first="S" last="Hassani">S. Hassani</name>
<affiliation wicri:level="1"><country xml:lang="fr">Algérie</country>
<wicri:regionArea>Centre de Recherche Nuclaire d'Alger, 2 Bd. Frantz Fanon, BP 399, 16000 Alger</wicri:regionArea>
<placeName><settlement type="city">Alger</settlement>
<region nuts="2">Wilaya d'Alger</region>
</placeName>
</affiliation>
</author>
<author><name sortKey="Maillard, J M" sort="Maillard, J M" uniqKey="Maillard J" first="J-M" last="Maillard">J-M Maillard</name>
<affiliation wicri:level="3"><country xml:lang="fr">France</country>
<wicri:regionArea>LPTMC, Universit de Paris 6, Tour 24, 4me tage, case 121, 4 Place Jussieu, 75252 Paris Cedex 05</wicri:regionArea>
<placeName><region type="region" nuts="2">Île-de-France</region>
<settlement type="city">Paris</settlement>
</placeName>
</affiliation>
<affiliation wicri:level="1"><country wicri:rule="url">France</country>
</affiliation>
</author>
<author><name sortKey="Zenine, N" sort="Zenine, N" uniqKey="Zenine N" first="N" last="Zenine">N. Zenine</name>
<affiliation wicri:level="1"><country xml:lang="fr">Algérie</country>
<wicri:regionArea>Centre de Recherche Nuclaire d'Alger, 2 Bd. Frantz Fanon, BP 399, 16000 Alger</wicri:regionArea>
<placeName><settlement type="city">Alger</settlement>
<region nuts="2">Wilaya d'Alger</region>
</placeName>
</affiliation>
<affiliation></affiliation>
</author>
</analytic>
<monogr></monogr>
<series><title level="j">Journal of Physics A: Mathematical and Theoretical</title>
<title level="j" type="abbrev">J. Phys. A: Math. Theor.</title>
<idno type="ISSN">1751-8113</idno>
<imprint><publisher>IOP Publishing</publisher>
<date type="published" when="2007">2007</date>
<biblScope unit="volume">40</biblScope>
<biblScope unit="issue">11</biblScope>
<biblScope unit="page" from="2583">2583</biblScope>
<biblScope unit="page" to="2614">2614</biblScope>
<biblScope unit="production">Printed in the UK</biblScope>
</imprint>
<idno type="ISSN">1751-8113</idno>
</series>
<idno type="istex">FF92A8B1E5A2C986F1E81D4B6C340ACA549EC532</idno>
<idno type="DOI">10.1088/1751-8113/40/11/001</idno>
<idno type="PII">S1751-8113(07)40171-8</idno>
<idno type="articleID">240171</idno>
<idno type="articleNumber">001</idno>
</biblStruct>
</sourceDesc>
<seriesStmt><idno type="ISSN">1751-8113</idno>
</seriesStmt>
</fileDesc>
<profileDesc><textClass></textClass>
<langUsage><language ident="en">en</language>
</langUsage>
</profileDesc>
</teiHeader>
<front><div type="abstract">We consider families of multiple and simple integrals of the Ising class and the linear ordinary differential equations with polynomial coefficients they are solutions of. We compare the full set of singularities given by the roots of the head polynomial of these linear ODEs and the subset of singularities occurring in the integrals, with the singularities obtained from the Landau conditions. For these Ising class integrals, we show that the Landau conditions can be worked out, either to give the singularities of the corresponding linear differential equation or the singularities occurring in the integral. The singular behaviour of these integrals is obtained in the self-dual variable w s/2/(1 s2), with s sinh(2K), where K J/kT is the usual Ising model coupling constant. Switching to the variable s, we show that the singularities of the analytic continuation of series expansions of these integrals actually break the KramersWannier duality. We revisit the singular behaviour (Zenine et al 2005 J. Phys. A: Math. Gen. 38 943974) of the third contribution to the magnetic susceptibility of Ising model (3) at the points 1 3w 4w2 0 and show that (3)(s) is not singular at the corresponding points inside the unit circle s 1, while its analytical continuation in the variable s is actually singular at the corresponding points 2 s s2 0 outside the unit circle (s > 1).</div>
</front>
</TEI>
<affiliations><list><country><li>Algérie</li>
<li>France</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>
</tree>
</affiliations>
</record>
Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Terre/explor/NickelMaghrebV1/Data/France/Analysis
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000177 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/France/Analysis/biblio.hfd -nk 000177 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien |wiki= Wicri/Terre |area= NickelMaghrebV1 |flux= France |étape= Analysis |type= RBID |clé= ISTEX:FF92A8B1E5A2C986F1E81D4B6C340ACA549EC532 |texte= Landau singularities and singularities of holonomic integrals of the Ising class }}
This area was generated with Dilib version V0.6.27. |