Generating configurations of increasing lattice size with machine learning and the inverse renormalization group

TL;DR

This paper reviews how machine learning, especially convolutional neural networks, enhances inverse renormalization group methods to generate larger lattice configurations efficiently, aiding studies in statistical mechanics and disordered systems.

Contribution

It introduces neural network-based inverse renormalization group transformations and demonstrates their application to complex models like the 3D Edwards-Anderson spin glass.

Findings

Neural networks can construct larger lattice configurations without critical slowing down.

Inverse renormalization group enables access to larger system sizes beyond supercomputing limits.

Applications shown in statistical mechanics, lattice field theory, and disordered systems.

Abstract

We review recent developments of machine learning algorithms pertinent to the inverse renormalization group, which was originally established as a generative numerical method by Ron-Swendsen-Brandt via the implementation of compatible Monte Carlo simulations. Inverse renormalization group methods enable the iterative generation of configurations for increasing lattice size without the critical slowing down effect. We discuss the construction of inverse renormalization group transformations with the use of convolutional neural networks and present applications in models of statistical mechanics, lattice field theory, and disordered systems. We highlight the case of the three-dimensional Edwards-Anderson spin glass, where the inverse renormalization group can be employed to construct configurations for lattice volumes that have not yet been accessed by dedicated supercomputers.