3D loop models and the CP^{n-1} sigma model
Many statistical mechanics problems can be framed in terms of random curves; we consider a class of three-dimensional loop models that are prototypes for such ensembles. The models show transitions between phases with infinite loops and short-loop phases. We map them to $CP^{n-1}$ sigma models, wher...
| Main Authors: | , , , , |
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| Format: | Journal article |
| Language: | English |
| Published: |
2011
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| _version_ | 1797101836328501248 |
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| author | Nahum, A Chalker, J Serna, P Ortuño, M Somoza, A |
| author_facet | Nahum, A Chalker, J Serna, P Ortuño, M Somoza, A |
| author_sort | Nahum, A |
| collection | OXFORD |
| description | Many statistical mechanics problems can be framed in terms of random curves; we consider a class of three-dimensional loop models that are prototypes for such ensembles. The models show transitions between phases with infinite loops and short-loop phases. We map them to $CP^{n-1}$ sigma models, where $n$ is the loop fugacity. Using Monte Carlo simulations, we find continuous transitions for $n=1,2,3$, and first order transitions for $n\geq 5$. The results are relevant to line defects in random media, as well as to Anderson localization and $(2+1)$-dimensional quantum magnets. |
| first_indexed | 2024-03-07T05:57:33Z |
| format | Journal article |
| id | oxford-uuid:eb0c11cd-afb8-445f-b9db-bba7c4aafdf5 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T05:57:33Z |
| publishDate | 2011 |
| record_format | dspace |
| spelling | oxford-uuid:eb0c11cd-afb8-445f-b9db-bba7c4aafdf52022-03-27T11:06:44Z3D loop models and the CP^{n-1} sigma modelJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:eb0c11cd-afb8-445f-b9db-bba7c4aafdf5EnglishSymplectic Elements at Oxford2011Nahum, AChalker, JSerna, POrtuño, MSomoza, AMany statistical mechanics problems can be framed in terms of random curves; we consider a class of three-dimensional loop models that are prototypes for such ensembles. The models show transitions between phases with infinite loops and short-loop phases. We map them to $CP^{n-1}$ sigma models, where $n$ is the loop fugacity. Using Monte Carlo simulations, we find continuous transitions for $n=1,2,3$, and first order transitions for $n\geq 5$. The results are relevant to line defects in random media, as well as to Anderson localization and $(2+1)$-dimensional quantum magnets. |
| spellingShingle | Nahum, A Chalker, J Serna, P Ortuño, M Somoza, A 3D loop models and the CP^{n-1} sigma model |
| title | 3D loop models and the CP^{n-1} sigma model |
| title_full | 3D loop models and the CP^{n-1} sigma model |
| title_fullStr | 3D loop models and the CP^{n-1} sigma model |
| title_full_unstemmed | 3D loop models and the CP^{n-1} sigma model |
| title_short | 3D loop models and the CP^{n-1} sigma model |
| title_sort | 3d loop models and the cp n 1 sigma model |
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