Computing critical exponents in 3D Ising model via pattern recognition/deep learning approach
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929576465137664 |
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| author | Burt, Timothy A. |
| author_facet | Burt, Timothy A. |
| contents | In this study, we computed three critical exponents ($α, β, γ$) for the 3D Ising model with Metropolis Algorithm using Finite-Size Scaling Analysis on six cube length scales (L=20,30,40,60,80,90), and performed a supervised Deep Learning (DL) approach (3D Convolutional Neural Network or CNN) to train a neural network on specific conformations of spin states. We find one can effectively reduce the information in thermodynamic ensemble-averaged quantities vs. reduced temperature t (magnetization per spin $<m>(t)$, specific heat per spin $<c>(t)$, magnetic susceptibility per spin $<χ>(t)$) to \textit{six} latent classes. We also demonstrate our CNN on a subset of L=20 conformations and achieve a train/test accuracy of 0.92 and 0.6875, respectively. However, more work remains to be done to quantify the feasibility of computing critical exponents from the output class labels (binned $m, c, χ$) from this approach and interpreting the results from DL models trained on systems in Condensed Matter Physics in general. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_02604 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Computing critical exponents in 3D Ising model via pattern recognition/deep learning approach Burt, Timothy A. Computational Physics Statistical Mechanics Artificial Intelligence Computer Vision and Pattern Recognition Machine Learning In this study, we computed three critical exponents ($α, β, γ$) for the 3D Ising model with Metropolis Algorithm using Finite-Size Scaling Analysis on six cube length scales (L=20,30,40,60,80,90), and performed a supervised Deep Learning (DL) approach (3D Convolutional Neural Network or CNN) to train a neural network on specific conformations of spin states. We find one can effectively reduce the information in thermodynamic ensemble-averaged quantities vs. reduced temperature t (magnetization per spin $<m>(t)$, specific heat per spin $<c>(t)$, magnetic susceptibility per spin $<χ>(t)$) to \textit{six} latent classes. We also demonstrate our CNN on a subset of L=20 conformations and achieve a train/test accuracy of 0.92 and 0.6875, respectively. However, more work remains to be done to quantify the feasibility of computing critical exponents from the output class labels (binned $m, c, χ$) from this approach and interpreting the results from DL models trained on systems in Condensed Matter Physics in general. |
| title | Computing critical exponents in 3D Ising model via pattern recognition/deep learning approach |
| topic | Computational Physics Statistical Mechanics Artificial Intelligence Computer Vision and Pattern Recognition Machine Learning |
| url | https://arxiv.org/abs/2411.02604 |