Principal component analysis of absorbing state phase transitions
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arXiv
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910826577788928 |
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| author | Muzzi, Cristiano Cortes, Ronald Santiago Bhakuni, Devendra Singh Jelić, Asja Gambassi, Andrea Dalmonte, Marcello Verdel, Roberto |
| author_facet | Muzzi, Cristiano Cortes, Ronald Santiago Bhakuni, Devendra Singh Jelić, Asja Gambassi, Andrea Dalmonte, Marcello Verdel, Roberto |
| contents | We perform a principal component analysis (PCA) of two one-dimensional lattice models belonging to distinct nonequilibrium universality classes - directed bond percolation and branching and annihilating random walks with even number of offspring. We find that the uncentered PCA of datasets storing various system's configurations can be successfully used to determine the critical properties of these nonequilibrium phase transitions. In particular, in both cases, we obtain good estimates of the critical point and the dynamical critical exponent of the models. For directed bond percolation we are, furthermore, able to extract critical exponents associated with the correlation length and the order parameter. We discuss the relation of our analysis with low-rank approximations of datasets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_12863 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Principal component analysis of absorbing state phase transitions Muzzi, Cristiano Cortes, Ronald Santiago Bhakuni, Devendra Singh Jelić, Asja Gambassi, Andrea Dalmonte, Marcello Verdel, Roberto Statistical Mechanics Disordered Systems and Neural Networks Data Analysis, Statistics and Probability We perform a principal component analysis (PCA) of two one-dimensional lattice models belonging to distinct nonequilibrium universality classes - directed bond percolation and branching and annihilating random walks with even number of offspring. We find that the uncentered PCA of datasets storing various system's configurations can be successfully used to determine the critical properties of these nonequilibrium phase transitions. In particular, in both cases, we obtain good estimates of the critical point and the dynamical critical exponent of the models. For directed bond percolation we are, furthermore, able to extract critical exponents associated with the correlation length and the order parameter. We discuss the relation of our analysis with low-rank approximations of datasets. |
| title | Principal component analysis of absorbing state phase transitions |
| topic | Statistical Mechanics Disordered Systems and Neural Networks Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2405.12863 |