Application of deep neural networks for computing the renormalization group flow of the two-dimensional phi^4 field theory
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| Format: | Preprint |
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2025
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| _version_ | 1866910173536190464 |
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| author | Zhao, Yueqi Fogler, Michael M. You, Yi-Zhuang |
| author_facet | Zhao, Yueqi Fogler, Michael M. You, Yi-Zhuang |
| contents | We introduce RGFlow, a deep neural network-based real-space renormalization group (RG) framework tailored for continuum scalar field theories. Leveraging generative capabilities of flow-based neural networks, RGFlow autonomously learns real-space RG transformations from data without prior knowledge of the underlying model. In contrast to conventional approaches, RGFlow is bijective (information-preserving) and is optimized based on the principle of minimal mutual information. We demonstrate the method on two examples. The first one is a one-dimensional Gaussian model, where RGFlow is shown to learn the classical decimation rule. The second is the two-dimensional phi^4 theory, where the network successfully identifies a Wilson-Fisher-like critical point and provides an estimate of the correlation-length critical exponent. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_06508 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Application of deep neural networks for computing the renormalization group flow of the two-dimensional phi^4 field theory Zhao, Yueqi Fogler, Michael M. You, Yi-Zhuang Disordered Systems and Neural Networks Statistical Mechanics We introduce RGFlow, a deep neural network-based real-space renormalization group (RG) framework tailored for continuum scalar field theories. Leveraging generative capabilities of flow-based neural networks, RGFlow autonomously learns real-space RG transformations from data without prior knowledge of the underlying model. In contrast to conventional approaches, RGFlow is bijective (information-preserving) and is optimized based on the principle of minimal mutual information. We demonstrate the method on two examples. The first one is a one-dimensional Gaussian model, where RGFlow is shown to learn the classical decimation rule. The second is the two-dimensional phi^4 theory, where the network successfully identifies a Wilson-Fisher-like critical point and provides an estimate of the correlation-length critical exponent. |
| title | Application of deep neural networks for computing the renormalization group flow of the two-dimensional phi^4 field theory |
| topic | Disordered Systems and Neural Networks Statistical Mechanics |
| url | https://arxiv.org/abs/2510.06508 |