Phase transitions in three-dimensional loop models and the CPn-1 sigma model
We consider the statistical mechanics of a class of models involving close-packed loops with fugacity n on three-dimensional lattices. The models exhibit phases of two types as a coupling constant is varied: in one, all loops are finite, and in the other, some loops are infinitely extended. We show...
| Main Authors: | , , , , |
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| Format: | Journal article |
| Language: | English |
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2013
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| _version_ | 1797089437062004736 |
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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 | We consider the statistical mechanics of a class of models involving close-packed loops with fugacity n on three-dimensional lattices. The models exhibit phases of two types as a coupling constant is varied: in one, all loops are finite, and in the other, some loops are infinitely extended. We show that the loop models are discretizations of CPn-1 σ models. The finite and infinite loop phases represent, respectively, disordered and ordered phases of the σ model, and we discuss the relationship between loop properties and σ model correlators. On large scales, loops are Brownian in an ordered phase and have a nontrivial fractal dimension at a critical point. We simulate the models, finding continuous transitions between the two phases for n=1,2,3 and first order transitions for n≥4. We also give a renormalization-group treatment of the CPn-1 model that shows how a continuous transition can survive for values of n larger than (but close to) 2, despite the presence of a cubic invariant in the Landau-Ginzburg description. The results we obtain are of broader relevance to a variety of problems, including SU(n) quantum magnets in (2+1) dimensions, Anderson localization in symmetry class C, and the statistics of random curves in three dimensions. © 2013 American Physical Society. |
| first_indexed | 2024-03-07T03:04:08Z |
| format | Journal article |
| id | oxford-uuid:b1f089cf-9416-4502-8c5f-d5de43f0c756 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T03:04:08Z |
| publishDate | 2013 |
| record_format | dspace |
| spelling | oxford-uuid:b1f089cf-9416-4502-8c5f-d5de43f0c7562022-03-27T04:07:54ZPhase transitions in three-dimensional loop models and the CPn-1 sigma modelJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:b1f089cf-9416-4502-8c5f-d5de43f0c756EnglishSymplectic Elements at Oxford2013Nahum, AChalker, JSerna, POrtuño, MSomoza, AWe consider the statistical mechanics of a class of models involving close-packed loops with fugacity n on three-dimensional lattices. The models exhibit phases of two types as a coupling constant is varied: in one, all loops are finite, and in the other, some loops are infinitely extended. We show that the loop models are discretizations of CPn-1 σ models. The finite and infinite loop phases represent, respectively, disordered and ordered phases of the σ model, and we discuss the relationship between loop properties and σ model correlators. On large scales, loops are Brownian in an ordered phase and have a nontrivial fractal dimension at a critical point. We simulate the models, finding continuous transitions between the two phases for n=1,2,3 and first order transitions for n≥4. We also give a renormalization-group treatment of the CPn-1 model that shows how a continuous transition can survive for values of n larger than (but close to) 2, despite the presence of a cubic invariant in the Landau-Ginzburg description. The results we obtain are of broader relevance to a variety of problems, including SU(n) quantum magnets in (2+1) dimensions, Anderson localization in symmetry class C, and the statistics of random curves in three dimensions. © 2013 American Physical Society. |
| spellingShingle | Nahum, A Chalker, J Serna, P Ortuño, M Somoza, A Phase transitions in three-dimensional loop models and the CPn-1 sigma model |
| title | Phase transitions in three-dimensional loop models and the CPn-1 sigma model |
| title_full | Phase transitions in three-dimensional loop models and the CPn-1 sigma model |
| title_fullStr | Phase transitions in three-dimensional loop models and the CPn-1 sigma model |
| title_full_unstemmed | Phase transitions in three-dimensional loop models and the CPn-1 sigma model |
| title_short | Phase transitions in three-dimensional loop models and the CPn-1 sigma model |
| title_sort | phase transitions in three dimensional loop models and the cpn 1 sigma model |
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