Finite-size analysis in neural network classification of critical phenomena

Area of Science:

• Statistical Physics
• Machine Learning
• Computational Physics

Background:

• Ferromagnetic phase transitions are critical phenomena studied in statistical physics.
• Supervised learning offers a novel approach to analyze these transitions.
• Understanding universality classes is key to characterizing phase transitions.

Purpose of the Study:

• To investigate the application of supervised learning for analyzing ferromagnetic phase transitions.
• To explore the relationship between neural network behavior and critical exponents.
• To determine if neural network outputs can accurately predict critical exponents.

Main Methods:

• Finite-size analysis of supervised learning results for the 2D Ising and Baxter-Wu models.
• Analyzing the variance of the neural network output function (VOF) as a function of temperature.
• Testing various neural network architectures, including fully connected, convolutional, and ResNet models.

Main Results:

• A peak in the VOF was observed in the critical region, correlating with the neural network's classification rate.
• The width of the VOF peak exhibited finite-size scaling, governed by the correlation length exponent (ν).
• Different neural network architectures were evaluated for their accuracy in extracting critical exponents.

Conclusions:

• Supervised learning provides a viable method for studying ferromagnetic phase transitions.
• The VOF's scaling behavior is directly linked to the universality class of the physical system.
• This approach offers a promising avenue for determining critical exponents in complex systems.