Deep learning of phase transitions with minimal examples.

Area of Science:

• Statistical physics
• Machine learning
• Computational physics

Background:

• Deep neural networks (DNNs) have shown promise in identifying phase transitions in physical systems.
• DNN predictions often mimic order parameters, aiding in locating critical temperatures (T_{c}) and estimating critical exponents.
• Convolutional neural networks (CNNs) are increasingly applied to analyze physical system configurations.

Purpose of the Study:

• To investigate the efficacy of a CNN in identifying critical parameters for the 2D Ising model.
• To assess the impact of restricted training data (only T=0 and T=∞) on CNN performance.
• To compare CNNs trained on extreme temperature data versus those trained on data across a temperature range.

Main Methods:

• Utilizing a convolutional neural network (CNN) architecture.
• Training the CNN on configurations of the 2D Ising model at T=0 and T=∞.
• Comparing the CNN's performance with a network trained on data from multiple temperatures below and above T_{c}.
• Analyzing the CNN's ability to identify T_{c} and critical exponents (ν, γ).

Main Results:

• The CNN trained on T=0 and T=∞ successfully identified the critical temperature (T_{c}) for the 2D Ising model.
• The critical exponent ν was also accurately estimated by the CNN trained on limited data.
• Extracting the critical exponent γ proved more challenging with the restricted training dataset.
• The network trained on limited data performed comparably to the network trained on extensive data for T_{c} and ν.

Conclusions:

• CNNs can effectively identify critical temperatures and certain critical exponents even with highly restricted training data.
• Extreme temperature training (T=0, T=∞) is a viable strategy for phase transition detection in some physical systems.
• Further research is needed to optimize CNNs for extracting all critical exponents, particularly γ, under data constraints.