Extracting Critical Exponent by Finite-Size Scaling with Convolutional Neural Networks

Abstract

Machine learning has been successfully applied to identify phases and phase transitions in condensed matter systems. However, quantitative characterization of the critical fluctuations near phase transitions is lacking. In this study we propose a finite-size scaling approach based on a convolutional neural network and analyze the critical behavior of a quantum Hall plateau transition. The localization length critical exponent learned by the neural network is consistent with the value obtained by conventional approaches. We show that the general-purposed method can be used to extract critical exponents in models with drastically different physics and input data, such as the two-dimensional Ising model and 4-state Potts model.

11 pages, 12 figures

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• Extending machine learning classification capabilities with histogram reweighting
• Can a CNN trained on the Ising model detect the phase transition of the $q$-state Potts model?
• Machine learning for percolation utilizing auxiliary Ising variables
• Machine Learning of Nonequilibrium Phase Transition in an Ising Model on Square Lattice
• Machine learning phase transitions of the three-dimensional Ising universality class
• Phase determination with and without deep learning
• Emergence of a finite-size-scaling function in the supervised learning of the Ising phase transition
• Learning What a Machine Learns in a Many-Body Localization Transition
• Discovering quasiorder parameters in the Potts model: A bridge between machine learning and critical phenomena
• Autonomous Discovery of the Ising Model's Critical Parameters with Reinforcement Learning
• Optimized Observable Readout from Single-shot Images of Ultracold Atoms via Machine Learning