Solving Statistical Mechanics Using Variational Autoregressive Networks.

Area of Science:

• Statistical Mechanics
• Machine Learning
• Computational Physics

Background:

• Traditional variational mean-field methods struggle with systems of finite size.
• Accurate calculation of normalized probabilities and direct sampling are challenging.
• Deep generative neural networks offer new possibilities for complex systems.

Purpose of the Study:

• To develop a general framework for solving statistical mechanics of finite-sized systems.
• To integrate autoregressive neural networks with variational mean-field approaches.
• To enable simultaneous computation of physical quantities and generation of samples.

Main Methods:

• Utilizing autoregressive neural networks within a variational mean-field framework.
• Implementing policy gradient methods from reinforcement learning for unbiased parameter gradient estimation.
• Applying the framework to benchmark models like 2D Ising, Hopfield, Sherrington-Kirkpatrick, and inverse Ising models.

Main Results:

• The proposed method allows for exact calculation of normalized probabilities and direct configuration sampling.
• It simultaneously computes variational free energy, entropy, magnetizations, and correlations.
• Demonstrated advantages over existing variational mean-field methods on classic statistical physics models.

Conclusions:

• This framework provides a powerful new tool for tackling statistical mechanics problems in finite-sized systems.
• The integration of deep generative neural networks offers significant advancements in the field.
• The approach facilitates efficient computation and sampling for complex physical models.