TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysCore.6.4.086
TI  - Non-parametric learning critical behavior in Ising partition functions: PCA entropy and intrinsic dimension
PY  - 2023/12/14
UR  - https://scipost.org/SciPostPhysCore.6.4.086
JF  - SciPost Physics Core
JA  - SciPost Phys. Core
VL  - 6
IS  - 4
SP  - 086
A1  - Panda, Rajat K.
AU  - Verdel, Roberto
AU  - Rodriguez, Alex
AU  - Sun, Hanlin
AU  - Bianconi, Ginestra
AU  - Dalmonte, Marcello
AB  - We provide and critically analyze a framework to learn critical behavior in classical partition functions through the application of non-parametric methods to data sets of thermal configurations. We illustrate our approach in phase transitions in 2D and 3D Ising models. First, we extend previous studies on the intrinsic dimension of 2D partition function data sets, by exploring the effect of volume in 3D Ising data. We find that as opposed to 2D systems for which this quantity has been successfully used in unsupervised characterizations of critical phenomena, in the 3D case its estimation is far more challenging. To circumvent this limitation, we then use the principal component analysis (PCA) entropy, a "Shannon entropy" of the normalized spectrum of the covariance matrix. We find a striking qualitative similarity to the thermodynamic entropy, which the PCA entropy approaches asymptotically. The latter allows us to extract-through a conventional finite-size scaling analysis with modest lattice sizes-the critical temperature with less than 1% error for both 2D and 3D models while being computationally efficient. The PCA entropy can readily be applied to characterize correlations and critical phenomena in a huge variety of many-body problems and suggests a (direct) link between easy-to-compute quantities and entropies.
ER  -

@Article{10.21468/SciPostPhysCore.6.4.086,
	title={{Non-parametric learning critical behavior in Ising partition functions: PCA entropy and intrinsic dimension}},
	author={Rajat K. Panda and Roberto Verdel and Alex Rodriguez and Hanlin Sun and Ginestra Bianconi and Marcello Dalmonte},
	journal={SciPost Phys. Core},
	volume={6},
	pages={086},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhysCore.6.4.086},
	url={https://scipost.org/10.21468/SciPostPhysCore.6.4.086},
}