Tensor Renormalization Group Calculations of Partition-Function Ratios
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912940934823936 |
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| author | Morita, Satoshi Kawashima, Naoki |
| author_facet | Morita, Satoshi Kawashima, Naoki |
| contents | The behavior of dimensionless quantities defined as ratios of partition functions is analyzed to investigate phase transitions and critical phenomena. At criticality, the universal values of these ratios can be predicted from conformal field theory (CFT) through the modular-invariant partition functions on a torus. We perform numerical calculations using the bond-weighted tensor renormalization group for three two-dimensional models belonging to different universality classes: the Ising model, the three-state Potts model, and the four-state Potts model. The partition-function ratios obey the same finite-size scaling form as the Binder parameter, and their critical values agree well with the universal values predicted by CFT. In the four-state Potts model, we observe logarithmic corrections in the system-size dependence of these ratios. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_03395 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tensor Renormalization Group Calculations of Partition-Function Ratios Morita, Satoshi Kawashima, Naoki Statistical Mechanics High Energy Physics - Lattice The behavior of dimensionless quantities defined as ratios of partition functions is analyzed to investigate phase transitions and critical phenomena. At criticality, the universal values of these ratios can be predicted from conformal field theory (CFT) through the modular-invariant partition functions on a torus. We perform numerical calculations using the bond-weighted tensor renormalization group for three two-dimensional models belonging to different universality classes: the Ising model, the three-state Potts model, and the four-state Potts model. The partition-function ratios obey the same finite-size scaling form as the Binder parameter, and their critical values agree well with the universal values predicted by CFT. In the four-state Potts model, we observe logarithmic corrections in the system-size dependence of these ratios. |
| title | Tensor Renormalization Group Calculations of Partition-Function Ratios |
| topic | Statistical Mechanics High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2512.03395 |