Vortex confinement transitions in the modified Goldstone model
The modified XY model is a variation of the XY model extended by a half-period term, exhibiting a rich phase structure. As the Goldstone model, also known as the linear O(2) model, can be obtained as a continuum and regular model for the XY model, we define the modified Goldstone model as that of th...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2020-01-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.2.013081 |
| _version_ | 1797211536437018624 |
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| author | Michikazu Kobayashi Gergely Fejős Chandrasekhar Chatterjee Muneto Nitta |
| author_facet | Michikazu Kobayashi Gergely Fejős Chandrasekhar Chatterjee Muneto Nitta |
| author_sort | Michikazu Kobayashi |
| collection | DOAJ |
| description | The modified XY model is a variation of the XY model extended by a half-period term, exhibiting a rich phase structure. As the Goldstone model, also known as the linear O(2) model, can be obtained as a continuum and regular model for the XY model, we define the modified Goldstone model as that of the modified XY model. We construct a vortex, a soliton (domain wall), and a molecule of two half-quantized vortices connected by a soliton as regular solutions of this model. Then we investigate its phase structure in two Euclidean dimensions via the functional renormalization group formalism and full numerical simulations. We argue that the field dependence of the wave function renormalization factor plays a crucial role in the existence of the line of fixed points describing the Berezinskii-Kosterlitz-Thouless (BKT) transition, which can ultimately terminate not only at one but at two end points in the modified model. This structure confirms that a two-step phase transition of the BKT and Ising types can occur in the system. We compare our renormalization group results with full numerical simulations, which also reveal that the phase transitions show a richer scenario than expected. |
| first_indexed | 2024-04-24T10:28:03Z |
| format | Article |
| id | doaj.art-6f2f4ea7569a44d8b7bd45fb10b16006 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:28:03Z |
| publishDate | 2020-01-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-6f2f4ea7569a44d8b7bd45fb10b160062024-04-12T16:49:10ZengAmerican Physical SocietyPhysical Review Research2643-15642020-01-012101308110.1103/PhysRevResearch.2.013081Vortex confinement transitions in the modified Goldstone modelMichikazu KobayashiGergely FejősChandrasekhar ChatterjeeMuneto NittaThe modified XY model is a variation of the XY model extended by a half-period term, exhibiting a rich phase structure. As the Goldstone model, also known as the linear O(2) model, can be obtained as a continuum and regular model for the XY model, we define the modified Goldstone model as that of the modified XY model. We construct a vortex, a soliton (domain wall), and a molecule of two half-quantized vortices connected by a soliton as regular solutions of this model. Then we investigate its phase structure in two Euclidean dimensions via the functional renormalization group formalism and full numerical simulations. We argue that the field dependence of the wave function renormalization factor plays a crucial role in the existence of the line of fixed points describing the Berezinskii-Kosterlitz-Thouless (BKT) transition, which can ultimately terminate not only at one but at two end points in the modified model. This structure confirms that a two-step phase transition of the BKT and Ising types can occur in the system. We compare our renormalization group results with full numerical simulations, which also reveal that the phase transitions show a richer scenario than expected.http://doi.org/10.1103/PhysRevResearch.2.013081 |
| spellingShingle | Michikazu Kobayashi Gergely Fejős Chandrasekhar Chatterjee Muneto Nitta Vortex confinement transitions in the modified Goldstone model Physical Review Research |
| title | Vortex confinement transitions in the modified Goldstone model |
| title_full | Vortex confinement transitions in the modified Goldstone model |
| title_fullStr | Vortex confinement transitions in the modified Goldstone model |
| title_full_unstemmed | Vortex confinement transitions in the modified Goldstone model |
| title_short | Vortex confinement transitions in the modified Goldstone model |
| title_sort | vortex confinement transitions in the modified goldstone model |
| url | http://doi.org/10.1103/PhysRevResearch.2.013081 |
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