jaxfss Reference Documentation

jaxfss is a neural finite-size scaling analysis package built on JAX, Flax, and Optax.

Finite-Size Scaling Analysis¶

The physical quantity near a critical point in a finite-size system obeys the scaling law:

where $A(T, L)$ is a physical quantity at temperature $T$ in a finite-size system of size $L$. $T_{\mathrm{c}}$ is the critical temperature, and $c_1$ and $c_2$ are critical exponents. Here $F[\cdot]$ is the unknown universal scaling function.

jaxfss estimates critical points and exponents by parameterizing the scaling function with a neural network and optimizing it end-to-end.

Related Packages¶

• BSA (C++): Finite-size scaling with Gaussian processes.

• FSS-tools (PyTorch): Finite-size scaling with neural networks and Gaussian processes.

Citation¶

Please cite our paper published in Physical Review E when using jaxfss:

• Ryosuke Yoneda and Kenji Harada, Neural network approach to scaling analysis of critical phenomena, Phys. Rev. E 107, 044128 (2023). Yoneda & Harada (2023)

@article{PhysRevE.107.044128,
  title = {Neural network approach to scaling analysis of critical phenomena},
  author = {Yoneda, Ryosuke and Harada, Kenji},
  journal = {Phys. Rev. E},
  volume = {107},
  issue = {4},
  pages = {044128},
  numpages = {10},
  year = {2023},
  month = {Apr},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevE.107.044128},
  url = {https://link.aps.org/doi/10.1103/PhysRevE.107.044128}
}