Deep learning on the 2-dimensional Ising model to extract the crossover region with a variational autoencoder

Area of Science:

• Statistical Mechanics
• Machine Learning Applications
• Computational Physics

Background:

• The 2-dimensional Ising model is a fundamental model in statistical mechanics.
• Understanding phase transitions, like ferromagnetic to paramagnetic, is crucial in condensed matter physics.
• Extracting information from complex systems often requires advanced analytical techniques.

Purpose of the Study:

• To investigate the 2-dimensional Ising model in a non-vanishing field using a variational autoencoder.
• To extract the crossover region between ferromagnetic and paramagnetic phases.
• To demonstrate machine learning's capability in analyzing complex physical systems.

Main Methods:

• Application of a variational autoencoder (VAE) to the 2D Ising model.
• Analysis of the encoded latent variable space for order and disorder metrics.
• Extraction of the critical point and configurational magnetizations.

Main Results:

• The latent variable space effectively tracks order and disorder in Ising configurations.
• A crossover region between phases was successfully extracted, consistent with theoretical expectations.
• The method achieved exceptional prediction accuracy for the critical point.
• Results show agreement with previously published data on configurational magnetizations.

Conclusions:

• Variational autoencoders provide suitable metrics for analyzing physical system configurations.
• Machine learning offers a powerful approach for extracting meaningful structural information from complex physical systems with limited a priori data.
• This method shows promise for future applications in condensed matter physics and beyond.