New renormalization group study of the 3-state Potts model and related statistical models
The critical behavior of three-state statistical models invariant under the full symmetry group S3 and its dependence on space dimension have been a matter of interest and debate. In particular, the phase transition of the 3-state Potts model in three dimensions is believed to be of the first order,...
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Elsevier
2025-02-01
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| Series: | Nuclear Physics B |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321325000112 |
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| author | José Gaite |
| author_facet | José Gaite |
| author_sort | José Gaite |
| collection | DOAJ |
| description | The critical behavior of three-state statistical models invariant under the full symmetry group S3 and its dependence on space dimension have been a matter of interest and debate. In particular, the phase transition of the 3-state Potts model in three dimensions is believed to be of the first order, without a definitive proof of absence of scale invariance in three-dimensional field theory with S3 symmetry. This scale invariance should appear as a non-trivial fixed point of the renormalization group, which has not been found. Our new search, with the non-perturbative renormalization group, finds such a fixed point, as a bifurcation from the trivial fixed point at the critical space dimension d=10/3, which extends continuously to d=3. It does not correspond to a second-order phase transition of the 3-state Potts model, but is interesting in its own right. In particular, it shows how the ε-expansion can fail. |
| format | Article |
| id | doaj-art-45065826037c4eb8b63c10423db8fd2e |
| institution | Kabale University |
| issn | 0550-3213 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj-art-45065826037c4eb8b63c10423db8fd2e2025-01-18T05:03:29ZengElsevierNuclear Physics B0550-32132025-02-011011116801New renormalization group study of the 3-state Potts model and related statistical modelsJosé Gaite0Applied Physics Dept., ETSIAE, Universidad Politécnica de Madrid, E-28040 Madrid, SpainThe critical behavior of three-state statistical models invariant under the full symmetry group S3 and its dependence on space dimension have been a matter of interest and debate. In particular, the phase transition of the 3-state Potts model in three dimensions is believed to be of the first order, without a definitive proof of absence of scale invariance in three-dimensional field theory with S3 symmetry. This scale invariance should appear as a non-trivial fixed point of the renormalization group, which has not been found. Our new search, with the non-perturbative renormalization group, finds such a fixed point, as a bifurcation from the trivial fixed point at the critical space dimension d=10/3, which extends continuously to d=3. It does not correspond to a second-order phase transition of the 3-state Potts model, but is interesting in its own right. In particular, it shows how the ε-expansion can fail.http://www.sciencedirect.com/science/article/pii/S0550321325000112Potts modelNon-perturbative renormalization groupBifurcations |
| spellingShingle | José Gaite New renormalization group study of the 3-state Potts model and related statistical models Nuclear Physics B Potts model Non-perturbative renormalization group Bifurcations |
| title | New renormalization group study of the 3-state Potts model and related statistical models |
| title_full | New renormalization group study of the 3-state Potts model and related statistical models |
| title_fullStr | New renormalization group study of the 3-state Potts model and related statistical models |
| title_full_unstemmed | New renormalization group study of the 3-state Potts model and related statistical models |
| title_short | New renormalization group study of the 3-state Potts model and related statistical models |
| title_sort | new renormalization group study of the 3 state potts model and related statistical models |
| topic | Potts model Non-perturbative renormalization group Bifurcations |
| url | http://www.sciencedirect.com/science/article/pii/S0550321325000112 |
| work_keys_str_mv | AT josegaite newrenormalizationgroupstudyofthe3statepottsmodelandrelatedstatisticalmodels |