Machine learning of phases and structures for model systems in physics

Abstract

The detection of phase transitions is a fundamental challenge in condensed matter physics, traditionally addressed through analytical methods and direct numerical simulations. In recent years, machine learning techniques have emerged as powerful tools to complement these standard approaches, offering valuable insights into phase and structure determination. Additionally, they have been shown to enhance the application of traditional methods. In this work, we review recent advancements in this area, with a focus on our contributions to phase and structure determination using supervised and unsupervised learning methods in several systems: (a) 2D site percolation, (b) the 3D Anderson model of localization, (c) the 2D $J_1$-$J_2$ Ising model, and (d) the prediction of large-angle convergent beam electron diffraction patterns.

15 two-column pages and 8 figures, invited review to the JPSJ issue of Special Topics "Machine Learning Physics"

References in corpus (35)

• Quantized Anomalous Hall Effect in Magnetic Topological Insulators
• Anderson Transitions
• Topological Anderson Insulator
• Unsupervised machine learning account of magnetic transitions in the Hubbard model
• Critical parameters from generalised multifractal analysis at the Anderson transition
• Deep Learning the Quantum Phase Transitions in Random Two-Dimensional Electron Systems
• Unsupervised phase discovery with deep anomaly detection
• Machine-Learning Studies on Spin Models
• Phase diagram of the Ising square lattice with competing interactions
• Accurate Computation of Quantum Excited States with Neural Networks
• Drawing Phase Diagrams of Random Quantum Systems by Deep Learning the Wave Functions
• Learning the Ising Model with Generative Neural Networks
• Unsupervised learning of topological phase transitions using Calinski-Harabaz index
• Deep Learning on the 2-Dimensional Ising Model to Extract the Crossover Region with a Variational Autoencoder
• Supervised and unsupervised learning of directed percolation
• Exploring neural network training strategies to determine phase transitions in frustrated magnetic models
• Phase diagram study of a two-dimensional frustrated antiferromagnet via unsupervised machine learning
• Phase Diagrams of Three-Dimensional Anderson and Quantum Percolation Models using Deep Three-Dimensional Convolutional Neural Network
• Interpretable and unsupervised phase classification
• Phase Object Reconstruction for 4D-STEM using Deep Learning
• Detecting ergodic bubbles at the crossover to many-body localization using neural networks
• Finite-size analysis in neural network classification of critical phenomena
• Neural Network flows of low q-state Potts and clock Models
• Can a CNN trained on the Ising model detect the phase transition of the $q$-state Potts model?
• Machine Learning Phase Diagram in the Half-filled One-dimensional Extended Hubbard Model
• Phase transition of Frustrated Ising model via D-wave Quantum Annealing Machine
• The percolating cluster is invisible to image recognition with deep learning
• Distinguishing Quantum Phases through Cusps in Full Counting Statistics
• Machine Learning of Nonequilibrium Phase Transition in an Ising Model on Square Lattice
• Machine Learning the Square-Lattice Ising Model
• Microscopic details of stripes and bubbles in the quantum Hall regime
• Non-monotonic behavior of the Binder Parameter in the discrete spin systems
• Minimalist Neural Networks training for phase classification in diluted-Ising models
• Machine learning the 2D percolation model
• Numerical methods for localization

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• Uncovering Magnetic Phases with Synthetic Data and Physics-Informed Training