Confusion scheme in machine learning detects double phase transitions and quasi-long-range order

Area of Science:

• Statistical Mechanics
• Machine Learning
• Computational Physics

Background:

• Supervised learning aids in studying critical phenomena but requires labeled data.
• Unsupervised learning offers a label-free alternative for analyzing complex systems.
• The confusion scheme is a proposed unsupervised method for identifying system properties.

Purpose of the Study:

• To investigate the efficacy of the confusion scheme in detecting phase transitions.
• To analyze systems with single and double phase transitions, including those with quasi-long-range order.
• To evaluate the performance of the confusion scheme across different models and system sizes.

Main Methods:

• Utilizing the confusion scheme from unsupervised machine learning.
• Applying Monte Carlo simulations to generate spin configuration data for various models (two-color Ashkin-Teller, XY, eight-state clock).
• Analyzing the size dependence of results to validate performance in the thermodynamic limit.

Main Results:

• The confusion scheme accurately approximates transition points for all tested models.
• Method accuracy increases with larger system sizes, confirming its validity in the thermodynamic limit.
• A distinct feature in the results correlates with the presence of quasi-long-range order.

Conclusions:

• The confusion scheme is a viable tool for detecting single and double phase transitions.
• This method is effective regardless of whether quasi-long-range order is present in the system.
• Unsupervised learning provides a powerful, label-free approach to critical phenomena analysis.