Unsupervised Machine Learning Method for the Phase Behavior of the Constant Magnetization Ising Model in Two and...

Area of Science:

• Computational Physics
• Statistical Mechanics
• Machine Learning Applications

Background:

• Phase transitions are critical phenomena studied using various methods.
• Machine learning offers unsupervised approaches, avoiding prior assumptions about phase transitions.
• Previous machine learning studies focused on critical behavior, not off-critical phase diagrams.

Purpose of the Study:

• To investigate the phase diagram of the Ising model at off-critical magnetizations using machine learning.
• To develop a robust machine learning method for analyzing phase transitions in 2D and 3D systems.
• To explore the effectiveness of local affinity as an input feature for machine learning models.

Main Methods:

• Utilized unsupervised machine learning, specifically a variational autoencoder.
• Introduced local affinity as a novel input feature, capturing spin and neighbor interactions.
• Applied the method to the 2D and 3D constant magnetization Ising models.

Main Results:

• The local affinity feature significantly improved phase behavior prediction accuracy.
• The variational autoencoder successfully predicted phase diagrams and critical exponent β.
• Results showed quantitative agreement with conventional simulation methods.

Conclusions:

• Local affinity is a robust and effective feature for machine learning analysis of phase transitions.
• The developed unsupervised method accurately characterizes phase diagrams in 2D and 3D Ising models.
• This approach is generalizable to various lattice and off-lattice systems.