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| Format: | Preprint |
| Publié: |
2024
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| Accès en ligne: | https://arxiv.org/abs/2407.15497 |
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| _version_ | 1866912192881754112 |
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| author | Gaite, Jose |
| author_facet | Gaite, Jose |
| contents | The critical behavior of three-state statistical models invariant under the full symmetry group $S_3$ 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 $S_3$ 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 $\varepsilon$-expansion can fail. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_15497 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | New renormalization group study of the 3-state Potts model and related statistical models Gaite, Jose Statistical Mechanics High Energy Physics - Theory The critical behavior of three-state statistical models invariant under the full symmetry group $S_3$ 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 $S_3$ 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 $\varepsilon$-expansion can fail. |
| title | New renormalization group study of the 3-state Potts model and related statistical models |
| topic | Statistical Mechanics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2407.15497 |