Machine Learning Phases of Matter

In this repository, we reproduce results from the paper by Carrasquilla and Melko titled Machine learning phases of matter.

Ferromagnetic Ising lattices are generated using the Metropolis algorithm for a variety of temperatures. A convolutional neural network is then trained directly on the spin configurations of the lattices and their corresponding phases.

Structure

The project is organized as follows:

├── data/
│   ├── square/ # Square lattices
│   │   ├── L10/ # Data for lattice side length, 10
│   │   │   └── lattices.pt
│   │   │   └── magnetizations.pt
│   │   │   └── temperatures.pt
│   │   ├── L20/
│   │   ├── L30/
│   │   ├── L40/
│   │   └── L60/
│   ├── triangular/ # Triangular lattices
│   │   ├── L10/ 
│   │   │   └── lattices.pt
│   │   │   └── magnetizations.pt
│   │   │   └── temperatures.pt
│   │   ├── L20/
│   │   ├── L30/
│   │   ├── L40/
│   │   └── L60/
├── figures/
├── data_gen.cpp
├── machine_learning.ipynb
├── requirements.txt
└── README.md

data_gen.cpp is used to generate the datasets under the data directory. Training on the datasets is performed in the machine_learning.ipynb notebook.

Set-up

Python

The following packages are required:

• Python 3.9+
• PyTorch
• Matplotlib

The essential Python packages can be installed here:

pip install -r requirements.txt

C++

The dataset is generated using a C++ script data_gen.cpp, which requires Libtorch, PyTorch's C++ library. You can follow the installation and set-up instructions for Libtorch from the official documentation.