A machine-learning study of phase transitions in Ising, Blume-Capel, and Ising-metamagnet models
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866913675344871424 |
|---|---|
| author | Babu, Vasanth Kumar Pandit, Rahul |
| author_facet | Babu, Vasanth Kumar Pandit, Rahul |
| contents | We combine machine-learning (ML) techniques with Monte Carlo (MC) simulations and finite-size scaling (FSS) to study continuous and first-order phase transitions in Ising, Blume-Capel, and Ising-metamagnet spin models. We go beyond earlier studies that had concentrated on obtaining the correlation-length exponent $ν$. In particular, we show (a) how to combine neural networks (NNs), trained with data from MC simulations of Ising-type spin models on finite lattices, with FSS to obtain both thermal magnetic exponents $y_t = 1/ν$ and $y_h$, respectively, at both critical and tricritical points, (b) how to obtain the NN counterpart of two-scale-factor universality at an Ising-type critical point, and (c) FSS at a first-order transition. We also obtain the FSS forms for the output of our trained NNs as functions of both the temperature and the magnetic field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_17815 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A machine-learning study of phase transitions in Ising, Blume-Capel, and Ising-metamagnet models Babu, Vasanth Kumar Pandit, Rahul Statistical Mechanics Computational Physics We combine machine-learning (ML) techniques with Monte Carlo (MC) simulations and finite-size scaling (FSS) to study continuous and first-order phase transitions in Ising, Blume-Capel, and Ising-metamagnet spin models. We go beyond earlier studies that had concentrated on obtaining the correlation-length exponent $ν$. In particular, we show (a) how to combine neural networks (NNs), trained with data from MC simulations of Ising-type spin models on finite lattices, with FSS to obtain both thermal magnetic exponents $y_t = 1/ν$ and $y_h$, respectively, at both critical and tricritical points, (b) how to obtain the NN counterpart of two-scale-factor universality at an Ising-type critical point, and (c) FSS at a first-order transition. We also obtain the FSS forms for the output of our trained NNs as functions of both the temperature and the magnetic field. |
| title | A machine-learning study of phase transitions in Ising, Blume-Capel, and Ising-metamagnet models |
| topic | Statistical Mechanics Computational Physics |
| url | https://arxiv.org/abs/2501.17815 |