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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| Format: | Article |
| Language: | English |
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Elsevier
2025-02-01
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| Series: | Nuclear Physics B |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321325000112 |
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| Summary: | 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. |
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| ISSN: | 0550-3213 |