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Machine-learning study of phase transitions in Ising, Blume-Capel, and Ising-metamagnet models
Vasanth Kumar Babu1, Rahul Pandit1
1Indian Institute of Science, Bangalore, Centre for Condensed Matter Theory, Department of Physics, 560012, India.
Physical Review. E
|August 1, 2025
Summary
This study integrates machine learning with simulations to analyze phase transitions in spin models. It introduces novel methods for calculating critical exponents and scaling functions, advancing our understanding of magnetic systems.
Area of Science:
- Statistical physics
- Computational physics
- Machine learning applications
Background:
- Traditional studies of phase transitions often focus on specific exponents like ν.
- Accurate determination of critical exponents (y_t, y_h) and scaling functions is crucial for understanding critical phenomena.
- Investigating universality and finite-size scaling (FSS) at different types of phase transitions (continuous and first-order) remains an active area of research.
Purpose of the Study:
- To develop and apply a novel framework combining neural networks (NNs) with Monte Carlo (MC) simulations and finite-size scaling (FSS).
- To extend the analysis beyond the correlation-length exponent (ν) to include thermal magnetic exponents (y_t, y_h) at critical and tricritical points.
- To investigate the applicability of this combined approach to different spin models and transition types, including first-order transitions.
Main Methods:
- Utilizing neural networks (NNs) trained on data from MC simulations of Ising-type spin models on finite lattices.
- Applying finite-size scaling (FSS) techniques in conjunction with NNs to extract critical exponents.
- Developing methods to obtain FSS for both continuous and first-order phase transitions, and for NN outputs as functions of temperature and magnetic field.
Main Results:
- Successfully combined NNs, MC simulations, and FSS to determine thermal magnetic exponents (y_t, y_h) at critical and tricritical points.
- Demonstrated the NN counterpart of two-scale-factor universality at an Ising-type critical point.
- Established FSS for first-order transitions and derived FSS forms for trained NN outputs.
Conclusions:
- The integration of machine learning with traditional simulation and scaling techniques offers a powerful new approach to studying phase transitions.
- This method advances the calculation of critical exponents and scaling functions, providing deeper insights into the behavior of magnetic spin systems.
- The framework is versatile, applicable to various spin models and transition types, paving the way for future research in computational statistical physics.
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