Walking, Weak first-order transitions, and Complex CFTs II. Two-dimensional Potts model at $Q>4$
We study complex CFTs describing fixed points of the two-dimensional $Q$-state Potts model with $Q>4$. Their existence is closely related to the weak first-order phase transition and walking RG behavior present in the real Potts model at $Q>4$. The Potts model, apart from its own significan...
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| Format: | Article |
| Language: | English |
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SciPost
2018-11-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.5.5.050 |
| _version_ | 1818996240722952192 |
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| author | Victor Gorbenko, Slava Rychkov, Bernardo Zan |
| author_facet | Victor Gorbenko, Slava Rychkov, Bernardo Zan |
| author_sort | Victor Gorbenko, Slava Rychkov, Bernardo Zan |
| collection | DOAJ |
| description | We study complex CFTs describing fixed points of the two-dimensional
$Q$-state Potts model with $Q>4$. Their existence is closely related to the
weak first-order phase transition and walking RG behavior present in the real
Potts model at $Q>4$. The Potts model, apart from its own significance, serves
as an ideal playground for testing this very general relation. Cluster
formulation provides nonperturbative definition for a continuous range of
parameter $Q$, while Coulomb gas description and connection to minimal models
provide some conformal data of the complex CFTs. We use one and two-loop
conformal perturbation theory around complex CFTs to compute various properties
of the real walking RG flow. These properties, such as drifting scaling
dimensions, appear to be common features of the QFTs with walking RG flows, and
can serve as a smoking gun for detecting walking in Monte Carlo simulations.
The complex CFTs discussed in this work are perfectly well defined, and can
in principle be seen in Monte Carlo simulations with complexified coupling
constants. In particular, we predict a pair of $S_5$-symmetric complex CFTs
with central charges $c\approx 1.138 \pm 0.021 i$ describing the fixed points
of a 5-state dilute Potts model with complexified temperature and vacancy
fugacity. |
| first_indexed | 2024-12-20T21:26:36Z |
| format | Article |
| id | doaj.art-e9ec9efaa9a8413bae929cc98badf666 |
| institution | Directory Open Access Journal |
| issn | 2542-4653 |
| language | English |
| last_indexed | 2024-12-20T21:26:36Z |
| publishDate | 2018-11-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj.art-e9ec9efaa9a8413bae929cc98badf6662022-12-21T19:26:08ZengSciPostSciPost Physics2542-46532018-11-015505010.21468/SciPostPhys.5.5.050Walking, Weak first-order transitions, and Complex CFTs II. Two-dimensional Potts model at $Q>4$Victor Gorbenko, Slava Rychkov, Bernardo ZanWe study complex CFTs describing fixed points of the two-dimensional $Q$-state Potts model with $Q>4$. Their existence is closely related to the weak first-order phase transition and walking RG behavior present in the real Potts model at $Q>4$. The Potts model, apart from its own significance, serves as an ideal playground for testing this very general relation. Cluster formulation provides nonperturbative definition for a continuous range of parameter $Q$, while Coulomb gas description and connection to minimal models provide some conformal data of the complex CFTs. We use one and two-loop conformal perturbation theory around complex CFTs to compute various properties of the real walking RG flow. These properties, such as drifting scaling dimensions, appear to be common features of the QFTs with walking RG flows, and can serve as a smoking gun for detecting walking in Monte Carlo simulations. The complex CFTs discussed in this work are perfectly well defined, and can in principle be seen in Monte Carlo simulations with complexified coupling constants. In particular, we predict a pair of $S_5$-symmetric complex CFTs with central charges $c\approx 1.138 \pm 0.021 i$ describing the fixed points of a 5-state dilute Potts model with complexified temperature and vacancy fugacity.https://scipost.org/SciPostPhys.5.5.050 |
| spellingShingle | Victor Gorbenko, Slava Rychkov, Bernardo Zan Walking, Weak first-order transitions, and Complex CFTs II. Two-dimensional Potts model at $Q>4$ SciPost Physics |
| title | Walking, Weak first-order transitions, and Complex CFTs II. Two-dimensional Potts model at $Q>4$ |
| title_full | Walking, Weak first-order transitions, and Complex CFTs II. Two-dimensional Potts model at $Q>4$ |
| title_fullStr | Walking, Weak first-order transitions, and Complex CFTs II. Two-dimensional Potts model at $Q>4$ |
| title_full_unstemmed | Walking, Weak first-order transitions, and Complex CFTs II. Two-dimensional Potts model at $Q>4$ |
| title_short | Walking, Weak first-order transitions, and Complex CFTs II. Two-dimensional Potts model at $Q>4$ |
| title_sort | walking weak first order transitions and complex cfts ii two dimensional potts model at q 4 |
| url | https://scipost.org/SciPostPhys.5.5.050 |
| work_keys_str_mv | AT victorgorbenkoslavarychkovbernardozan walkingweakfirstordertransitionsandcomplexcftsiitwodimensionalpottsmodelatq4 |