On four-point connectivities in the critical 2d Potts model
We perform Monte-Carlo computations of four-point cluster connectivities in the critical 2d Potts model, for numbers of states $Q\in (0,4)$ that are not necessarily integer. We compare these connectivities to four-point functions in a CFT that interpolates between D-series minimal models. We find...
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| Format: | Article |
| Language: | English |
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SciPost
2019-10-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.7.4.044 |
| _version_ | 1811227407181414400 |
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| author | Marco Picco, Sylvain Ribault, Raoul Santachiara |
| author_facet | Marco Picco, Sylvain Ribault, Raoul Santachiara |
| author_sort | Marco Picco, Sylvain Ribault, Raoul Santachiara |
| collection | DOAJ |
| description | We perform Monte-Carlo computations of four-point cluster connectivities in
the critical 2d Potts model, for numbers of states $Q\in (0,4)$ that are not
necessarily integer. We compare these connectivities to four-point functions in
a CFT that interpolates between D-series minimal models. We find that 3
combinations of the 4 independent connectivities agree with CFT four-point
functions, down to the $2$ to $4$ significant digits of our Monte-Carlo
computations. However, we argue that the agreement is exact only in the special
cases $Q=0, 3, 4$. We conjecture that the Potts model can be analytically
continued to a double cover of the half-plane $\{\Re c <13\}$, where $c$ is the
central charge of the Virasoro symmetry algebra. |
| first_indexed | 2024-04-12T09:42:02Z |
| format | Article |
| id | doaj.art-2f671a160a784803a94df28a13220af0 |
| institution | Directory Open Access Journal |
| issn | 2542-4653 |
| language | English |
| last_indexed | 2024-04-12T09:42:02Z |
| publishDate | 2019-10-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj.art-2f671a160a784803a94df28a13220af02022-12-22T03:38:03ZengSciPostSciPost Physics2542-46532019-10-017404410.21468/SciPostPhys.7.4.044On four-point connectivities in the critical 2d Potts modelMarco Picco, Sylvain Ribault, Raoul SantachiaraWe perform Monte-Carlo computations of four-point cluster connectivities in the critical 2d Potts model, for numbers of states $Q\in (0,4)$ that are not necessarily integer. We compare these connectivities to four-point functions in a CFT that interpolates between D-series minimal models. We find that 3 combinations of the 4 independent connectivities agree with CFT four-point functions, down to the $2$ to $4$ significant digits of our Monte-Carlo computations. However, we argue that the agreement is exact only in the special cases $Q=0, 3, 4$. We conjecture that the Potts model can be analytically continued to a double cover of the half-plane $\{\Re c <13\}$, where $c$ is the central charge of the Virasoro symmetry algebra.https://scipost.org/SciPostPhys.7.4.044 |
| spellingShingle | Marco Picco, Sylvain Ribault, Raoul Santachiara On four-point connectivities in the critical 2d Potts model SciPost Physics |
| title | On four-point connectivities in the critical 2d Potts model |
| title_full | On four-point connectivities in the critical 2d Potts model |
| title_fullStr | On four-point connectivities in the critical 2d Potts model |
| title_full_unstemmed | On four-point connectivities in the critical 2d Potts model |
| title_short | On four-point connectivities in the critical 2d Potts model |
| title_sort | on four point connectivities in the critical 2d potts model |
| url | https://scipost.org/SciPostPhys.7.4.044 |
| work_keys_str_mv | AT marcopiccosylvainribaultraoulsantachiara onfourpointconnectivitiesinthecritical2dpottsmodel |