FSS-tools

The finite-size scaling (FSS) method is a powerful tool for getting universal information of critical phenomena. It estimates universal information from observables of critical phenomena at finite-size systems.

Here, we introduce an implementation with PyTorch of two FSS methods by using Gaussian process (GP) and a neural network (NN).

Install

We prepare the fss_torch module to apply a FSS method by GP or NN in src/fss_torch.

Prerequisites

The module PyTorch and GPyTorch are required.

Quickstart

To use our FSS methods by GP and NN, see the following jupyter notebooks in examples.

• FSS method by GP
• FSS method by NN

Related sites

• FSS method by GP with C++
• FSS method by NN with Python (JAX/Flex)

Citations

1. Kenji Harada: Bayesian inference in the scaling analysis of critical phenomena, Physical Review E 84 (2011) 056704.
   DOI: 10.1103/PhysRevE.84.056704
2. Kenji Harada: Kernel method for corrections to scaling, Physical Review E 92 (2015) 012106.
   DOI: 10.1103/PhysRevE.92.012106
3. Ryosuke Yoneda and Kenji Harada : Neural Network Approach to Scaling Analysis of Critical Phenomena, arXiv:2209.01777.

History

• March 14, 2022: The first release (v0.1.0)