Peierls Transition in Gross-Neveu Model from Bethe Ansatz
The two-dimensional Gross-Neveu model is anticipated to undergo a crystalline phase transition at high baryon charge densities. This conclusion is drawn from the mean-field approximation, which closely resembles models of Peierls instability. We demonstrate that this transition indeed occurs when bo...
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| creator | Melin, Valdemar Sekiguchi, Yuta Wiegmann, Paul Zarembo, Konstantin |
| description | The two-dimensional Gross-Neveu model is anticipated to undergo a crystalline
phase transition at high baryon charge densities. This conclusion is drawn from
the mean-field approximation, which closely resembles models of Peierls
instability. We demonstrate that this transition indeed occurs when both the
rank of the symmetry group and the dimension of the particle representation
contributing to the baryon density are large (the large-N limit). We derive
this result through the exact solution of the model, developing the large-N
limit of the Bethe Ansatz. Our analytical construction of the large-N solution
of the Bethe Ansatz equations aligns perfectly with the periodic (finite-gap)
solution of the Korteweg-de Vries (KdV) of the mean-field analysis. |
| doi_str_mv | 10.48550/arxiv.2404.07307 |
| format | Article |
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phase transition at high baryon charge densities. This conclusion is drawn from
the mean-field approximation, which closely resembles models of Peierls
instability. We demonstrate that this transition indeed occurs when both the
rank of the symmetry group and the dimension of the particle representation
contributing to the baryon density are large (the large-N limit). We derive
this result through the exact solution of the model, developing the large-N
limit of the Bethe Ansatz. Our analytical construction of the large-N solution
of the Bethe Ansatz equations aligns perfectly with the periodic (finite-gap)
solution of the Korteweg-de Vries (KdV) of the mean-field analysis.</description><identifier>DOI: 10.48550/arxiv.2404.07307</identifier><language>eng</language><subject>Physics - High Energy Physics - Theory</subject><creationdate>2024-04</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2404.07307$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2404.07307$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Melin, Valdemar</creatorcontrib><creatorcontrib>Sekiguchi, Yuta</creatorcontrib><creatorcontrib>Wiegmann, Paul</creatorcontrib><creatorcontrib>Zarembo, Konstantin</creatorcontrib><title>Peierls Transition in Gross-Neveu Model from Bethe Ansatz</title><description>The two-dimensional Gross-Neveu model is anticipated to undergo a crystalline
phase transition at high baryon charge densities. This conclusion is drawn from
the mean-field approximation, which closely resembles models of Peierls
instability. We demonstrate that this transition indeed occurs when both the
rank of the symmetry group and the dimension of the particle representation
contributing to the baryon density are large (the large-N limit). We derive
this result through the exact solution of the model, developing the large-N
limit of the Bethe Ansatz. Our analytical construction of the large-N solution
of the Bethe Ansatz equations aligns perfectly with the periodic (finite-gap)
solution of the Korteweg-de Vries (KdV) of the mean-field analysis.</description><subject>Physics - High Energy Physics - Theory</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotj71OwzAURr0woMIDMOEXSLj-j8dSQUFqgSF7dONcC0tpguxQAU8PFKazfDr6DmNXAmrdGAM3mD_SsZYadA1OgTtn_oUS5bHwNuNU0pLmiaeJb_NcSvVER3rn-3mgkcc8H_gtLa_E11PB5euCnUUcC13-c8Xa-7t281DtnrePm_WuQutcZXXvVe-sAbSoXGh8MCCDs7YRAWMMKHshfpbSWGm8F41yUQPFISpAHNSKXf9pT9-7t5wOmD-734bu1KC-AXgbQFM</recordid><startdate>20240410</startdate><enddate>20240410</enddate><creator>Melin, Valdemar</creator><creator>Sekiguchi, Yuta</creator><creator>Wiegmann, Paul</creator><creator>Zarembo, Konstantin</creator><scope>GOX</scope></search><sort><creationdate>20240410</creationdate><title>Peierls Transition in Gross-Neveu Model from Bethe Ansatz</title><author>Melin, Valdemar ; Sekiguchi, Yuta ; Wiegmann, Paul ; Zarembo, Konstantin</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a677-64b93b7650a6a37c89c502c76681caffca2b1167725625991837f40efdf30aad3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Physics - High Energy Physics - Theory</topic><toplevel>online_resources</toplevel><creatorcontrib>Melin, Valdemar</creatorcontrib><creatorcontrib>Sekiguchi, Yuta</creatorcontrib><creatorcontrib>Wiegmann, Paul</creatorcontrib><creatorcontrib>Zarembo, Konstantin</creatorcontrib><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Melin, Valdemar</au><au>Sekiguchi, Yuta</au><au>Wiegmann, Paul</au><au>Zarembo, Konstantin</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Peierls Transition in Gross-Neveu Model from Bethe Ansatz</atitle><date>2024-04-10</date><risdate>2024</risdate><abstract>The two-dimensional Gross-Neveu model is anticipated to undergo a crystalline
phase transition at high baryon charge densities. This conclusion is drawn from
the mean-field approximation, which closely resembles models of Peierls
instability. We demonstrate that this transition indeed occurs when both the
rank of the symmetry group and the dimension of the particle representation
contributing to the baryon density are large (the large-N limit). We derive
this result through the exact solution of the model, developing the large-N
limit of the Bethe Ansatz. Our analytical construction of the large-N solution
of the Bethe Ansatz equations aligns perfectly with the periodic (finite-gap)
solution of the Korteweg-de Vries (KdV) of the mean-field analysis.</abstract><doi>10.48550/arxiv.2404.07307</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Physics - High Energy Physics - Theory |
| title | Peierls Transition in Gross-Neveu Model from Bethe Ansatz |
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