Tensor Renormalization Group Calculations of Partition-Function Ratios
smorita / bwtrg-ratio-z
Overview
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.
- URL
- https://isspns-gitlab.issp.u-tokyo.ac.jp/smorita/bwtrg-ratio-z
- DOI
- 10.7566/JPSJ.95.044001
- Citations
- 3 (OpenAlex, as of 2026-10-05)
- Authors
- Satoshi Morita, Naoki Kawashima
- License
- CC BY 4.0
- Keywords
- partition function ratiostensor renormalization groupphase transitionscritical phenomenaconformal field theorymodular invariant partition functionstorus partition functionIsing model (keywords of the paper, from OpenAlex)
- Category
- Others
- References
- J. Phys. Soc. Jpn. 95, 044001 (2026)
- Contact
- smorita__at__keio.jp, kawashima__at__issp.u-tokyo.ac.jp (Please replace __at__ with @.)
- Note
- https://arxiv.org/abs/2512.03395
Paper and citation
If you use this data, please cite the following paper.
Satoshi Morita and Naoki Kawashima, "Tensor Renormalization Group Calculations of Partition-Function Ratios", Journal of the Physical Society of Japan 95(4) (2026). https://doi.org/10.7566/JPSJ.95.044001
Show BibTeX
@article{Morita_2026, title={Tensor Renormalization Group Calculations of Partition-Function Ratios}, volume={95}, ISSN={1347-4073}, url={http://dx.doi.org/10.7566/jpsj.95.044001}, DOI={10.7566/jpsj.95.044001}, number={4}, journal={Journal of the Physical Society of Japan}, publisher={Physical Society of Japan}, author={Morita, Satoshi and Kawashima, Naoki}, year={2026}, month=Apr }Bibliographic details and the open-access link are from OpenAlex; the BibTeX is from doi.org (as registered by the publisher).
README
Tensor renormalization group calculations of partition-function ratios
About
The dimensionless quantities defined from the partition function ratio can reveal extensive information about phase transitions and critical phenomena.
This repository contains the computational results obtained by the bond-weighted tensor renormalization group method (BWTRG), as presented in our paper.
License
We would be grateful if you cite our paper when publishing results using our data in this repository.
Satoshi Morita and Naoki Kawashima, "Tensor renormalization group calculations of partition-function ratios", J. Phys. Soc. Jpn. 95, 044001 (2026)
https://doi.org/10.7566/JPSJ.95.044001
Folder structures
See data/README.md for more information on the data.
Source code
The BWTRG source code for generating data in this repository will be provided upon request.
A simple BWTRG code for the 2D Ising model is available at [this repository](https://github.com/smorita/TRG_Ising_2D].
Contact
- Satoshi Morita <smorita__at__keio.jp> (Corresponding Author)
- Naoki Kawashima <kawashima__at__issp.u-tokyo.ac.jp>
please replace __at__ by @.
Source: https://isspns-gitlab.issp.u-tokyo.ac.jp/smorita/bwtrg-ratio-z README