{"title":"在无限 N 极限通过玻色两点函数重新审视 (1+1) 维手性格罗斯-涅乌模型中的空间不均匀凝聚态","authors":"Adrian Koenigstein, Marc Winstel","doi":"10.1088/1751-8121/ad6721","DOIUrl":null,"url":null,"abstract":"This work shows that the known phase boundary between the phase with chiral symmetry and the phase of spatially inhomogeneous chiral symmetry breaking in the phase diagram of the <inline-formula>\n<tex-math><?CDATA $(1 + 1)$?></tex-math>\n<mml:math overflow=\"scroll\"><mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math>\n<inline-graphic xlink:href=\"aad6721ieqn2.gif\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula>-dimensional chiral Gross–Neveu (GN) model can be detected from the bosonic two-point function alone and thereby confirms and extends previous results (Schön and Thies 2000 <italic toggle=\"yes\">At The Frontier of Particle Physics: Handbook of QCD, Boris Ioffe Festschrift</italic> vol 3 (World Scentific) ch 33, pp 1945–2032; Boehmer <italic toggle=\"yes\">et al</italic> 2008 <italic toggle=\"yes\">Phys. Rev.</italic> D <bold>78</bold> 065043; Boehmer and Thies 2009 <italic toggle=\"yes\">Phys. Rev.</italic> D <bold>80</bold> 125038; Thies 2018 <italic toggle=\"yes\">Phys. Rev.</italic> D <bold>98</bold> 096019; Thies 2022 <italic toggle=\"yes\">Phys. Rev.</italic> D <bold>105</bold> 116003). The analysis is referred to as the stability analysis of the symmetric phase and does not require knowledge about spatial modulations of condensates. We perform this analysis in the infinite-<italic toggle=\"yes\">N</italic> limit at nonzero temperature and nonzero quark and chiral chemical potentials also inside the inhomogeneous phase. Thereby we observe an interesting relation between the bosonic 1-particle irreducible two-point vertex function of the chiral GN model and the spinodal line of the GN model.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"145 1","pages":""},"PeriodicalIF":2.0000,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Revisiting the spatially inhomogeneous condensates in the (1+1) -dimensional chiral Gross–Neveu model via the bosonic two-point function in the infinite-N limit\",\"authors\":\"Adrian Koenigstein, Marc Winstel\",\"doi\":\"10.1088/1751-8121/ad6721\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This work shows that the known phase boundary between the phase with chiral symmetry and the phase of spatially inhomogeneous chiral symmetry breaking in the phase diagram of the <inline-formula>\\n<tex-math><?CDATA $(1 + 1)$?></tex-math>\\n<mml:math overflow=\\\"scroll\\\"><mml:mrow><mml:mo stretchy=\\\"false\\\">(</mml:mo><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=\\\"false\\\">)</mml:mo></mml:mrow></mml:math>\\n<inline-graphic xlink:href=\\\"aad6721ieqn2.gif\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula>-dimensional chiral Gross–Neveu (GN) model can be detected from the bosonic two-point function alone and thereby confirms and extends previous results (Schön and Thies 2000 <italic toggle=\\\"yes\\\">At The Frontier of Particle Physics: Handbook of QCD, Boris Ioffe Festschrift</italic> vol 3 (World Scentific) ch 33, pp 1945–2032; Boehmer <italic toggle=\\\"yes\\\">et al</italic> 2008 <italic toggle=\\\"yes\\\">Phys. Rev.</italic> D <bold>78</bold> 065043; Boehmer and Thies 2009 <italic toggle=\\\"yes\\\">Phys. Rev.</italic> D <bold>80</bold> 125038; Thies 2018 <italic toggle=\\\"yes\\\">Phys. Rev.</italic> D <bold>98</bold> 096019; Thies 2022 <italic toggle=\\\"yes\\\">Phys. Rev.</italic> D <bold>105</bold> 116003). The analysis is referred to as the stability analysis of the symmetric phase and does not require knowledge about spatial modulations of condensates. We perform this analysis in the infinite-<italic toggle=\\\"yes\\\">N</italic> limit at nonzero temperature and nonzero quark and chiral chemical potentials also inside the inhomogeneous phase. Thereby we observe an interesting relation between the bosonic 1-particle irreducible two-point vertex function of the chiral GN model and the spinodal line of the GN model.\",\"PeriodicalId\":16763,\"journal\":{\"name\":\"Journal of Physics A: Mathematical and Theoretical\",\"volume\":\"145 1\",\"pages\":\"\"},\"PeriodicalIF\":2.0000,\"publicationDate\":\"2024-08-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Physics A: Mathematical and Theoretical\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1088/1751-8121/ad6721\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Physics A: Mathematical and Theoretical","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1088/1751-8121/ad6721","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
Revisiting the spatially inhomogeneous condensates in the (1+1) -dimensional chiral Gross–Neveu model via the bosonic two-point function in the infinite-N limit
This work shows that the known phase boundary between the phase with chiral symmetry and the phase of spatially inhomogeneous chiral symmetry breaking in the phase diagram of the (1+1)-dimensional chiral Gross–Neveu (GN) model can be detected from the bosonic two-point function alone and thereby confirms and extends previous results (Schön and Thies 2000 At The Frontier of Particle Physics: Handbook of QCD, Boris Ioffe Festschrift vol 3 (World Scentific) ch 33, pp 1945–2032; Boehmer et al 2008 Phys. Rev. D 78 065043; Boehmer and Thies 2009 Phys. Rev. D 80 125038; Thies 2018 Phys. Rev. D 98 096019; Thies 2022 Phys. Rev. D 105 116003). The analysis is referred to as the stability analysis of the symmetric phase and does not require knowledge about spatial modulations of condensates. We perform this analysis in the infinite-N limit at nonzero temperature and nonzero quark and chiral chemical potentials also inside the inhomogeneous phase. Thereby we observe an interesting relation between the bosonic 1-particle irreducible two-point vertex function of the chiral GN model and the spinodal line of the GN model.
期刊介绍:
Publishing 50 issues a year, Journal of Physics A: Mathematical and Theoretical is a major journal of theoretical physics reporting research on the mathematical structures that describe fundamental processes of the physical world and on the analytical, computational and numerical methods for exploring these structures.