An integrable 3D lattice model with positive Boltzmann weights
In this paper we construct a three-dimensional (3D) solvable lattice model with non-negative Boltzmann weights. The spin variables in the model are assigned to edges of the 3D cubic lattice and run over an infinite number of discrete states. The Boltzmann weights satisfy the tetrahedron equation, wh...
Gespeichert in:
| Veröffentlicht in: | Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2013-11, Vol.46 (46), p.465206-16 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 16 |
|---|---|
| container_issue | 46 |
| container_start_page | 465206 |
| container_title | Journal of physics. A, Mathematical and theoretical |
| container_volume | 46 |
| creator | Mangazeev, Vladimir V Bazhanov, Vladimir V Sergeev, Sergey M |
| description | In this paper we construct a three-dimensional (3D) solvable lattice model with non-negative Boltzmann weights. The spin variables in the model are assigned to edges of the 3D cubic lattice and run over an infinite number of discrete states. The Boltzmann weights satisfy the tetrahedron equation, which is a 3D generalization of the Yang-Baxter equation. The weights depend on a free parameter 0 < q < 1 and three continuous field variables. The layer-to-layer transfer matrices of the model form a two-parameter commutative family. This is the first example of a non-trivial solvable 3D lattice model with non-negative Boltzmann weights. |
| doi_str_mv | 10.1088/1751-8113/46/46/465206 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_1669912638</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1669912638</sourcerecordid><originalsourceid>FETCH-LOGICAL-c331t-49f394376bb8bc99c68754e0a75400cb6e60f7be901b22e705cb9b39da9f17773</originalsourceid><addsrcrecordid>eNqFkE9LxDAQxYMouK5-BcnRS92kaZPmIqzrX1jwoueQZKe7WdqmNqmLfnpbungVHjMD897A_BC6puSWkqJYUJHTpKCULTI-KU8JP0Gz4yKlp38zZefoIoQ9IXlGZDpDd8sGuybCttOmAswecKVjdBZw7TdQ4YOLO9z64KL7Anzvq_hT66bBB3DbXQyX6KzUVYCrY5-jj6fH99VLsn57fl0t14lljMYkkyWTGRPcmMJYKS0vRJ4B0UMlxBoOnJTCgCTUpCkIklsjDZMbLUsqhGBzdDPdbTv_2UOIqnbBQlXpBnwfFOVcSppyVgxWPllt50PooFRt52rdfStK1AhMjSzUyEJlfNIIbAimU9D5Vu193zXDR_-FfgGZn2vX</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1669912638</pqid></control><display><type>article</type><title>An integrable 3D lattice model with positive Boltzmann weights</title><source>IOP Publishing Journals</source><source>Institute of Physics (IOP) Journals - HEAL-Link</source><creator>Mangazeev, Vladimir V ; Bazhanov, Vladimir V ; Sergeev, Sergey M</creator><creatorcontrib>Mangazeev, Vladimir V ; Bazhanov, Vladimir V ; Sergeev, Sergey M</creatorcontrib><description>In this paper we construct a three-dimensional (3D) solvable lattice model with non-negative Boltzmann weights. The spin variables in the model are assigned to edges of the 3D cubic lattice and run over an infinite number of discrete states. The Boltzmann weights satisfy the tetrahedron equation, which is a 3D generalization of the Yang-Baxter equation. The weights depend on a free parameter 0 < q < 1 and three continuous field variables. The layer-to-layer transfer matrices of the model form a two-parameter commutative family. This is the first example of a non-trivial solvable 3D lattice model with non-negative Boltzmann weights.</description><identifier>ISSN: 1751-8113</identifier><identifier>EISSN: 1751-8121</identifier><identifier>DOI: 10.1088/1751-8113/46/46/465206</identifier><identifier>CODEN: JPHAC5</identifier><language>eng</language><publisher>IOP Publishing</publisher><subject>Construction ; Cubic lattice ; integrable systems ; Lattices ; Mathematical analysis ; Mathematical models ; q-oscillator algebra ; tetrahedron equation ; Tetrahedrons ; Three dimensional ; Three dimensional models ; Transfer matrices</subject><ispartof>Journal of physics. A, Mathematical and theoretical, 2013-11, Vol.46 (46), p.465206-16</ispartof><rights>2013 IOP Publishing Ltd</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c331t-49f394376bb8bc99c68754e0a75400cb6e60f7be901b22e705cb9b39da9f17773</citedby><cites>FETCH-LOGICAL-c331t-49f394376bb8bc99c68754e0a75400cb6e60f7be901b22e705cb9b39da9f17773</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://iopscience.iop.org/article/10.1088/1751-8113/46/46/465206/pdf$$EPDF$$P50$$Giop$$H</linktopdf><link.rule.ids>314,776,780,27901,27902,53821,53868</link.rule.ids></links><search><creatorcontrib>Mangazeev, Vladimir V</creatorcontrib><creatorcontrib>Bazhanov, Vladimir V</creatorcontrib><creatorcontrib>Sergeev, Sergey M</creatorcontrib><title>An integrable 3D lattice model with positive Boltzmann weights</title><title>Journal of physics. A, Mathematical and theoretical</title><addtitle>JPhysA</addtitle><addtitle>J. Phys. A: Math. Theor</addtitle><description>In this paper we construct a three-dimensional (3D) solvable lattice model with non-negative Boltzmann weights. The spin variables in the model are assigned to edges of the 3D cubic lattice and run over an infinite number of discrete states. The Boltzmann weights satisfy the tetrahedron equation, which is a 3D generalization of the Yang-Baxter equation. The weights depend on a free parameter 0 < q < 1 and three continuous field variables. The layer-to-layer transfer matrices of the model form a two-parameter commutative family. This is the first example of a non-trivial solvable 3D lattice model with non-negative Boltzmann weights.</description><subject>Construction</subject><subject>Cubic lattice</subject><subject>integrable systems</subject><subject>Lattices</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>q-oscillator algebra</subject><subject>tetrahedron equation</subject><subject>Tetrahedrons</subject><subject>Three dimensional</subject><subject>Three dimensional models</subject><subject>Transfer matrices</subject><issn>1751-8113</issn><issn>1751-8121</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><recordid>eNqFkE9LxDAQxYMouK5-BcnRS92kaZPmIqzrX1jwoueQZKe7WdqmNqmLfnpbungVHjMD897A_BC6puSWkqJYUJHTpKCULTI-KU8JP0Gz4yKlp38zZefoIoQ9IXlGZDpDd8sGuybCttOmAswecKVjdBZw7TdQ4YOLO9z64KL7Anzvq_hT66bBB3DbXQyX6KzUVYCrY5-jj6fH99VLsn57fl0t14lljMYkkyWTGRPcmMJYKS0vRJ4B0UMlxBoOnJTCgCTUpCkIklsjDZMbLUsqhGBzdDPdbTv_2UOIqnbBQlXpBnwfFOVcSppyVgxWPllt50PooFRt52rdfStK1AhMjSzUyEJlfNIIbAimU9D5Vu193zXDR_-FfgGZn2vX</recordid><startdate>20131122</startdate><enddate>20131122</enddate><creator>Mangazeev, Vladimir V</creator><creator>Bazhanov, Vladimir V</creator><creator>Sergeev, Sergey M</creator><general>IOP Publishing</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7U5</scope><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope></search><sort><creationdate>20131122</creationdate><title>An integrable 3D lattice model with positive Boltzmann weights</title><author>Mangazeev, Vladimir V ; Bazhanov, Vladimir V ; Sergeev, Sergey M</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c331t-49f394376bb8bc99c68754e0a75400cb6e60f7be901b22e705cb9b39da9f17773</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2013</creationdate><topic>Construction</topic><topic>Cubic lattice</topic><topic>integrable systems</topic><topic>Lattices</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>q-oscillator algebra</topic><topic>tetrahedron equation</topic><topic>Tetrahedrons</topic><topic>Three dimensional</topic><topic>Three dimensional models</topic><topic>Transfer matrices</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Mangazeev, Vladimir V</creatorcontrib><creatorcontrib>Bazhanov, Vladimir V</creatorcontrib><creatorcontrib>Sergeev, Sergey M</creatorcontrib><collection>CrossRef</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Journal of physics. A, Mathematical and theoretical</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Mangazeev, Vladimir V</au><au>Bazhanov, Vladimir V</au><au>Sergeev, Sergey M</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>An integrable 3D lattice model with positive Boltzmann weights</atitle><jtitle>Journal of physics. A, Mathematical and theoretical</jtitle><stitle>JPhysA</stitle><addtitle>J. Phys. A: Math. Theor</addtitle><date>2013-11-22</date><risdate>2013</risdate><volume>46</volume><issue>46</issue><spage>465206</spage><epage>16</epage><pages>465206-16</pages><issn>1751-8113</issn><eissn>1751-8121</eissn><coden>JPHAC5</coden><abstract>In this paper we construct a three-dimensional (3D) solvable lattice model with non-negative Boltzmann weights. The spin variables in the model are assigned to edges of the 3D cubic lattice and run over an infinite number of discrete states. The Boltzmann weights satisfy the tetrahedron equation, which is a 3D generalization of the Yang-Baxter equation. The weights depend on a free parameter 0 < q < 1 and three continuous field variables. The layer-to-layer transfer matrices of the model form a two-parameter commutative family. This is the first example of a non-trivial solvable 3D lattice model with non-negative Boltzmann weights.</abstract><pub>IOP Publishing</pub><doi>10.1088/1751-8113/46/46/465206</doi><tpages>16</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1751-8113 |
| ispartof | Journal of physics. A, Mathematical and theoretical, 2013-11, Vol.46 (46), p.465206-16 |
| issn | 1751-8113 1751-8121 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_1669912638 |
| source | IOP Publishing Journals; Institute of Physics (IOP) Journals - HEAL-Link |
| subjects | Construction Cubic lattice integrable systems Lattices Mathematical analysis Mathematical models q-oscillator algebra tetrahedron equation Tetrahedrons Three dimensional Three dimensional models Transfer matrices |
| title | An integrable 3D lattice model with positive Boltzmann weights |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-15T02%3A52%3A09IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=An%20integrable%203D%20lattice%20model%20with%20positive%20Boltzmann%20weights&rft.jtitle=Journal%20of%20physics.%20A,%20Mathematical%20and%20theoretical&rft.au=Mangazeev,%20Vladimir%20V&rft.date=2013-11-22&rft.volume=46&rft.issue=46&rft.spage=465206&rft.epage=16&rft.pages=465206-16&rft.issn=1751-8113&rft.eissn=1751-8121&rft.coden=JPHAC5&rft_id=info:doi/10.1088/1751-8113/46/46/465206&rft_dat=%3Cproquest_cross%3E1669912638%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=1669912638&rft_id=info:pmid/&rfr_iscdi=true |