Machine learning domain adaptation in spin models with continuous phase transitions.

Area of Science:

• Statistical Mechanics
• Machine Learning Applications
• Computational Physics

Background:

• Understanding universality classes is key in statistical mechanics.
• Neural networks offer novel approaches to analyze complex physical systems.
• Transfer learning in physics aims to leverage trained models across different systems.

Purpose of the Study:

• To investigate the transferability of neural networks trained on spin lattice models.
• To assess network performance in predicting critical properties (critical temperature, correlation length exponent) across different universality classes.
• To determine the conditions under which neural network models exhibit universality.

Main Methods:

• Supervised learning applied to three 2D models: Ising, four-state Potts, and Baxter-Wu.
• Utilized datasets of spin configurations and binding energy configurations.
• Performed direct training/testing and cross-testing between models.

Main Results:

• Critical temperature estimates showed good agreement with known values for direct training.
• Cross-testing critical temperature estimates between the four-state Potts and Ising models using energy datasets were less accurate.
• Critical length exponent estimates were less consistent, with energy datasets yielding more accurate results in some cross-testing scenarios (e.g., Ising and Baxter-Wu models).

Conclusions:

• Neural networks show promise for estimating critical temperatures but require careful consideration for transfer learning.
• Predicting correlation length exponents across different universality classes remains challenging.
• The choice of dataset (spin vs. energy) significantly impacts transfer learning performance in critical phenomena analysis.