Integrability as a consequence of discrete holomorphicity: the ZN model
Identifieur interne : 005B35 ( Main/Exploration ); précédent : 005B34; suivant : 005B36Integrability as a consequence of discrete holomorphicity: the ZN model
Auteurs : I. T. Alam [Australie] ; M. T. Bachelor [Australie]Source :
- Journal of physics. A, Mathematical and theoretical : (Print) [ 1751-8113 ] ; 2012.
Descripteurs français
- Pascal (Inist)
English descriptors
Abstract
It has recently been established that imposing the condition of discrete holomorphicity on a lattice parafermionic observable leads to the critical Boltzmann weights in a number of lattice models. Remarkably, the solutions of these linear equations also solve the Yang-Baxter equations. We extend this analysis for the ZN model by explicitly considering the condition of discrete holomorphicity on two and three adjacent rhombi. For two rhombi this leads to a quadratic equation in the Boltzmann weights and for three rhombi a cubic equation. The two-rhombus equation implies the inversion relations. The star- triangle relation follows from the three-rhombus equation. We also show that these weights are self-dual as a consequence of discrete holomorphicity.
Affiliations:
Links toward previous steps (curation, corpus...)
- to stream PascalFrancis, to step Corpus: 000C33
- to stream PascalFrancis, to step Curation: 005232
- to stream PascalFrancis, to step Checkpoint: 001001
- to stream Main, to step Merge: 005E36
- to stream Main, to step Curation: 005B35
Le document en format XML
<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en" level="a">Integrability as a consequence of discrete holomorphicity: the Z<sub>N</sub> model</title><author><name sortKey="Alam, I T" sort="Alam, I T" uniqKey="Alam I" first="I. T." last="Alam">I. T. Alam</name><affiliation wicri:level="1"><inist:fA14 i1="01"><s1>Department of Theoretical Physics, Research School of Physics and Engineering, The Australian National University</s1><s2>Canberra ACT 0200</s2><s3>AUS</s3><sZ>1 aut.</sZ><sZ>2 aut.</sZ></inist:fA14><country>Australie</country><wicri:noRegion>Canberra ACT 0200</wicri:noRegion></affiliation></author><author><name sortKey="Bachelor, M T" sort="Bachelor, M T" uniqKey="Bachelor M" first="M. T." last="Bachelor">M. T. Bachelor</name><affiliation wicri:level="1"><inist:fA14 i1="01"><s1>Department of Theoretical Physics, Research School of Physics and Engineering, The Australian National University</s1><s2>Canberra ACT 0200</s2><s3>AUS</s3><sZ>1 aut.</sZ><sZ>2 aut.</sZ></inist:fA14><country>Australie</country><wicri:noRegion>Canberra ACT 0200</wicri:noRegion></affiliation><affiliation wicri:level="1"><inist:fA14 i1="02"><s1>Mathematical Sciences Institute, The Australian National University</s1><s2>Canberra ACT 0200</s2><s3>AUS</s3><sZ>2 aut.</sZ></inist:fA14><country>Australie</country><wicri:noRegion>Canberra ACT 0200</wicri:noRegion></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">INIST</idno><idno type="inist">13-0080443</idno><date when="2012">2012</date><idno type="stanalyst">PASCAL 13-0080443 INIST</idno><idno type="RBID">Pascal:13-0080443</idno><idno type="wicri:Area/PascalFrancis/Corpus">000C33</idno><idno type="wicri:Area/PascalFrancis/Curation">005232</idno><idno type="wicri:Area/PascalFrancis/Checkpoint">001001</idno><idno type="wicri:explorRef" wicri:stream="PascalFrancis" wicri:step="Checkpoint">001001</idno><idno type="wicri:doubleKey">1751-8113:2012:Alam I:integrability:as:a</idno><idno type="wicri:Area/Main/Merge">005E36</idno><idno type="wicri:Area/Main/Curation">005B35</idno><idno type="wicri:Area/Main/Exploration">005B35</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a">Integrability as a consequence of discrete holomorphicity: the Z<sub>N</sub> model</title><author><name sortKey="Alam, I T" sort="Alam, I T" uniqKey="Alam I" first="I. T." last="Alam">I. T. Alam</name><affiliation wicri:level="1"><inist:fA14 i1="01"><s1>Department of Theoretical Physics, Research School of Physics and Engineering, The Australian National University</s1><s2>Canberra ACT 0200</s2><s3>AUS</s3><sZ>1 aut.</sZ><sZ>2 aut.</sZ></inist:fA14><country>Australie</country><wicri:noRegion>Canberra ACT 0200</wicri:noRegion></affiliation></author><author><name sortKey="Bachelor, M T" sort="Bachelor, M T" uniqKey="Bachelor M" first="M. T." last="Bachelor">M. T. Bachelor</name><affiliation wicri:level="1"><inist:fA14 i1="01"><s1>Department of Theoretical Physics, Research School of Physics and Engineering, The Australian National University</s1><s2>Canberra ACT 0200</s2><s3>AUS</s3><sZ>1 aut.</sZ><sZ>2 aut.</sZ></inist:fA14><country>Australie</country><wicri:noRegion>Canberra ACT 0200</wicri:noRegion></affiliation><affiliation wicri:level="1"><inist:fA14 i1="02"><s1>Mathematical Sciences Institute, The Australian National University</s1><s2>Canberra ACT 0200</s2><s3>AUS</s3><sZ>2 aut.</sZ></inist:fA14><country>Australie</country><wicri:noRegion>Canberra ACT 0200</wicri:noRegion></affiliation></author></analytic><series><title level="j" type="main">Journal of physics. A, Mathematical and theoretical : (Print)</title><title level="j" type="abbreviated">J. phys., A, math. theor. : (Print)</title><idno type="ISSN">1751-8113</idno><imprint><date when="2012">2012</date></imprint></series></biblStruct></sourceDesc><seriesStmt><title level="j" type="main">Journal of physics. A, Mathematical and theoretical : (Print)</title><title level="j" type="abbreviated">J. phys., A, math. theor. : (Print)</title><idno type="ISSN">1751-8113</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Integrability</term><term>Lattice model</term><term>Quadratic equation</term><term>Yang Baxter equation</term></keywords><keywords scheme="Pascal" xml:lang="fr"><term>Intégrabilité</term><term>Modèle réticulaire</term><term>Equation Yang Baxter</term><term>Equation quadratique</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">It has recently been established that imposing the condition of discrete holomorphicity on a lattice parafermionic observable leads to the critical Boltzmann weights in a number of lattice models. Remarkably, the solutions of these linear equations also solve the Yang-Baxter equations. We extend this analysis for the Z<sub>N</sub> model by explicitly considering the condition of discrete holomorphicity on two and three adjacent rhombi. For two rhombi this leads to a quadratic equation in the Boltzmann weights and for three rhombi a cubic equation. The two-rhombus equation implies the inversion relations. The star- triangle relation follows from the three-rhombus equation. We also show that these weights are self-dual as a consequence of discrete holomorphicity.</div></front></TEI><affiliations><list><country><li>Australie</li></country></list><tree><country name="Australie"><noRegion><name sortKey="Alam, I T" sort="Alam, I T" uniqKey="Alam I" first="I. T." last="Alam">I. T. Alam</name></noRegion><name sortKey="Bachelor, M T" sort="Bachelor, M T" uniqKey="Bachelor M" first="M. T." last="Bachelor">M. T. Bachelor</name><name sortKey="Bachelor, M T" sort="Bachelor, M T" uniqKey="Bachelor M" first="M. T." last="Bachelor">M. T. Bachelor</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Asie/explor/AustralieFrV1/Data/Main/Exploration
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 005B35 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Main/Exploration/biblio.hfd -nk 005B35 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien
|wiki= Wicri/Asie
|area= AustralieFrV1
|flux= Main
|étape= Exploration
|type= RBID
|clé= Pascal:13-0080443
|texte= Integrability as a consequence of discrete holomorphicity: the ZN model
}}
| This area was generated with Dilib version V0.6.33. |  |