Tensor renormalization group approach to critical phenomena via symmetry-twisted partition functions
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915911169998848 |
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| author | Akiyama, Shinichiro Jha, Raghav G. Maeda, Jun Tanizaki, Yuya Unmuth-Yockey, Judah |
| author_facet | Akiyama, Shinichiro Jha, Raghav G. Maeda, Jun Tanizaki, Yuya Unmuth-Yockey, Judah |
| contents | The locality of field theories strongly constrains the possible behaviors of symmetry-twisted partition functions, and thus they serve as order parameters to detect low-energy realizations of global symmetries, such as spontaneous symmetry breaking (SSB). We demonstrate that the tensor renormalization group (TRG) offers an efficient framework to compute the symmetry-twisted partition functions, which enables us to detect the symmetry-breaking transition and also to study associated critical phenomena. As concrete examples of SSB, we investigate the two-dimensional (2D) classical Ising model and the three-dimensional (3D) classical $O(2)$ nonlinear sigma model, and we identify their critical points solely from the twisted partition function. By employing the finite-size scaling argument, we find the critical temperature $T_c=2.2017(2)$ with the critical exponent $ν= 0.663(33)$ for the 3D $O(2)$ model. In addition, we also study the Berezinskii-Kosterlitz-Thouless (BKT) criticality of the 2D classical $O(2)$ model by extracting the helicity modulus from the twisted partition functions, and we obtain the BKT transition temperature, $T_{\mathrm{BKT}}=0.8928(2)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_02681 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Tensor renormalization group approach to critical phenomena via symmetry-twisted partition functions Akiyama, Shinichiro Jha, Raghav G. Maeda, Jun Tanizaki, Yuya Unmuth-Yockey, Judah High Energy Physics - Lattice Statistical Mechanics High Energy Physics - Theory The locality of field theories strongly constrains the possible behaviors of symmetry-twisted partition functions, and thus they serve as order parameters to detect low-energy realizations of global symmetries, such as spontaneous symmetry breaking (SSB). We demonstrate that the tensor renormalization group (TRG) offers an efficient framework to compute the symmetry-twisted partition functions, which enables us to detect the symmetry-breaking transition and also to study associated critical phenomena. As concrete examples of SSB, we investigate the two-dimensional (2D) classical Ising model and the three-dimensional (3D) classical $O(2)$ nonlinear sigma model, and we identify their critical points solely from the twisted partition function. By employing the finite-size scaling argument, we find the critical temperature $T_c=2.2017(2)$ with the critical exponent $ν= 0.663(33)$ for the 3D $O(2)$ model. In addition, we also study the Berezinskii-Kosterlitz-Thouless (BKT) criticality of the 2D classical $O(2)$ model by extracting the helicity modulus from the twisted partition functions, and we obtain the BKT transition temperature, $T_{\mathrm{BKT}}=0.8928(2)$. |
| title | Tensor renormalization group approach to critical phenomena via symmetry-twisted partition functions |
| topic | High Energy Physics - Lattice Statistical Mechanics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2601.02681 |