Phase diagram study of a two-dimensional frustrated antiferromagnet via unsupervised machine learning

Abstract

We apply unsupervised learning techniques to classify the different phases of the $J_1-J_2$ antiferromagnetic Ising model on the honeycomb lattice. We construct the phase diagram of the system using convolutional autoencoders. These neural networks can detect phase transitions in the system via `anomaly detection', without the need for any label or a priori knowledge of the phases. We present different ways of training these autoencoders and we evaluate them to discriminate between distinct magnetic phases. In this process, we highlight the case of high temperature or even random training data. Finally, we analyze the capability of the autoencoder to detect the ground state degeneracy through the reconstruction error.

11 pages, 15 figures

References in corpus (12)

• Learning phase transitions by confusion
• Self-Learning Monte Carlo Method
• Unsupervised machine learning account of magnetic transitions in the Hubbard model
• Unsupervised Learning of Frustrated Classical Spin Models I: Principle Component Analysis
• Unsupervised phase discovery with deep anomaly detection
• beta-Cu2V2O7: a spin-1/2 honeycomb lattice system
• Disordered Ground State and Magnetic Field-Induced Long-Range Order in an S=3/2 Antiferromagnetic Honeycomb Lattice Compound Bi3Mn4O12(NO3)
• Phase diagram of the Ising square lattice with competing interactions
• Exotic disordered phases in the quantum $J_1-J_2$ model on the honeycomb lattice
• Location of the Potts-critical end point in the frustrated Ising model on the square lattice
• Unsupervised machine learning of quantum phase transitions using diffusion maps
• Monte Carlo studies of the Ising square lattice with competing interactions

Cited by in corpus (14)

• Critical properties of the frustrated Ising model on a honeycomb lattice: A Monte Carlo study
• Spiral-spin-liquid behaviors and persistent reciprocal kagomé structure in frustrated van der Waals magnets and beyond
• Unsupervised machine learning approaches to the $q$-state Potts model
• Unsupervised learning of phase transitions via modified anomaly detection with autoencoders
• Machine Learning of Nonequilibrium Phase Transition in an Ising Model on Square Lattice
• Machine Learning the Square-Lattice Ising Model
• Machine learning of phases and structures for model systems in physics
• Phase determination with and without deep learning
• Minimalist Neural Networks training for phase classification in diluted-Ising models
• Topological and magnetic properties of the interacting Bernevig-Hughes-Zhang model
• Global exploration of phase behavior in frustrated Ising models using unsupervised learning techniques
• Frustrated Ising model on the honeycomb lattice: Metastability and universality
• Uncovering Magnetic Phases with Synthetic Data and Physics-Informed Training
• Large-Angle Convergent-Beam Electron Diffraction Patterns via Conditional Generative Adversarial Networks