Simulating first-order phase transition with hierarchical autoregressive networks.

Area of Science:

• Statistical mechanics
• Computational physics
• Machine learning applications

Background:

• Phase transitions in statistical models are crucial for understanding material properties.
• Traditional algorithms like the Wolff cluster algorithm face challenges in efficiency near critical points.
• Neural network approaches offer potential for improved simulation techniques.

Purpose of the Study:

• To introduce and evaluate a hierarchical autoregressive neural network sampling algorithm for the 2D Q-state Potts model.
• To compare its performance against the Wolff cluster algorithm near a first-order phase transition.
• To demonstrate the effectiveness of pretraining for large neural network training.

Main Methods:

• Application of a hierarchical autoregressive neural network sampling algorithm.
• Simulations conducted around the phase transition of the 2D Q-state Potts model at Q=12.
• Introduction and utilization of a pretraining technique for neural network efficiency.
• Comparison with the Wolff cluster algorithm.

Main Results:

• Significant improvement in statistical uncertainty compared to the Wolff cluster algorithm at similar computational cost.
• Demonstrated effectiveness of the pretraining technique for training large neural networks.
• Accurate estimation of free energy and entropy near the phase transition.

Conclusions:

• The hierarchical autoregressive neural network approach offers superior performance for simulating systems with bimodal distributions, particularly near phase transitions.
• Pretraining is a viable strategy for efficiently training large neural networks in this context.
• The method provides highly precise estimates for thermodynamic quantities like free energy and entropy.