Emerging Jordan blocks in the two-dimensional Potts and loop models at generic $Q$
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2024
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| author | Liu, Lawrence Jacobsen, Jesper Lykke Saleur, Hubert |
| author_facet | Liu, Lawrence Jacobsen, Jesper Lykke Saleur, Hubert |
| contents | It was recently suggested -- based on general self-consistency arguments as well as results from the bootstrap (arXiv:2005.07708, arXiv:2007.11539, arXiv:2007.04190) -- that the CFT describing the $Q$-state Potts model is logarithmic for generic values of $Q$, with rank-two Jordan blocks for $L_0$ and ${\mkern 1.5mu\overline{\mkern-1.5mu L\mkern-1.5mu}\mkern 1.5mu}_0$ in many sectors of the theory. This is despite the well-known fact that the lattice transfer matrix (or Hamiltonian) is diagonalizable in (arbitrary) finite size. While the emergence of Jordan blocks only in the limit $L\to\infty$ is perfectly possible conceptually, diagonalizability in finite size makes the measurement of logarithmic couplings (whose values are analytically predicted in arXiv:2007.11539, arXiv:2007.04190) very challenging. This problem is solved in the present paper (which can be considered a companion to arXiv:2007.11539), and the conjectured logarithmic structure of the CFT confirmed in detail by the study of the lattice model and associated "emerging Jordan blocks." |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_19830 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Emerging Jordan blocks in the two-dimensional Potts and loop models at generic $Q$ Liu, Lawrence Jacobsen, Jesper Lykke Saleur, Hubert Mathematical Physics Statistical Mechanics High Energy Physics - Theory It was recently suggested -- based on general self-consistency arguments as well as results from the bootstrap (arXiv:2005.07708, arXiv:2007.11539, arXiv:2007.04190) -- that the CFT describing the $Q$-state Potts model is logarithmic for generic values of $Q$, with rank-two Jordan blocks for $L_0$ and ${\mkern 1.5mu\overline{\mkern-1.5mu L\mkern-1.5mu}\mkern 1.5mu}_0$ in many sectors of the theory. This is despite the well-known fact that the lattice transfer matrix (or Hamiltonian) is diagonalizable in (arbitrary) finite size. While the emergence of Jordan blocks only in the limit $L\to\infty$ is perfectly possible conceptually, diagonalizability in finite size makes the measurement of logarithmic couplings (whose values are analytically predicted in arXiv:2007.11539, arXiv:2007.04190) very challenging. This problem is solved in the present paper (which can be considered a companion to arXiv:2007.11539), and the conjectured logarithmic structure of the CFT confirmed in detail by the study of the lattice model and associated "emerging Jordan blocks." |
| title | Emerging Jordan blocks in the two-dimensional Potts and loop models at generic $Q$ |
| topic | Mathematical Physics Statistical Mechanics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2403.19830 |