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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.19425 |
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| _version_ | 1866917816107532288 |
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| author | Morikawa, Okuto Tanaka, Mizuki Kitazawa, Masakiyo Suzuki, Hiroshi |
| author_facet | Morikawa, Okuto Tanaka, Mizuki Kitazawa, Masakiyo Suzuki, Hiroshi |
| contents | We present the lattice simulation of the renormalization group flow in the $3$-dimensional $O(N)$ linear sigma model. This model possesses a nontrivial infrared fixed point, called Wilson--Fisher fixed point. Arguing that the parameter space of running coupling constants can be spanned by expectation values of operators evolved by the gradient flow, we exemplify a scaling behavior analysis based on the gradient flow in the large $N$ approximation at criticality. Then, we work out the numerical simulation of the theory with finite $N$. Depicting the renormalization group flow along the gradient flow, we confirm the existence of the Wilson--Fisher fixed point non-perturbatively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_19425 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lattice study of RG fixed point based on gradient flow in $3$D $O(N)$ sigma model Morikawa, Okuto Tanaka, Mizuki Kitazawa, Masakiyo Suzuki, Hiroshi High Energy Physics - Lattice We present the lattice simulation of the renormalization group flow in the $3$-dimensional $O(N)$ linear sigma model. This model possesses a nontrivial infrared fixed point, called Wilson--Fisher fixed point. Arguing that the parameter space of running coupling constants can be spanned by expectation values of operators evolved by the gradient flow, we exemplify a scaling behavior analysis based on the gradient flow in the large $N$ approximation at criticality. Then, we work out the numerical simulation of the theory with finite $N$. Depicting the renormalization group flow along the gradient flow, we confirm the existence of the Wilson--Fisher fixed point non-perturbatively. |
| title | Lattice study of RG fixed point based on gradient flow in $3$D $O(N)$ sigma model |
| topic | High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2410.19425 |