Principal component analysis of absorbing state phase transitions

TL;DR

This paper demonstrates that principal component analysis applied to system configurations can effectively identify critical points and exponents in nonequilibrium phase transitions, offering a data-driven approach to studying complex systems.

Contribution

The study introduces a PCA-based method to determine critical properties of nonequilibrium phase transitions from configuration data, providing estimates of critical points and exponents.

Findings

Successfully estimated critical points and dynamical critical exponents.

Extracted correlation length and order parameter exponents for directed bond percolation.

Showed PCA's effectiveness in analyzing different universality classes.

Abstract

We perform a principal component analysis (PCA) of two one-dimensional lattice models belonging to distinct nonequilibrium universality classes - directed bond percolation and branching and annihilating random walks with even number of offspring. We find that the uncentered PCA of datasets storing various system's configurations can be successfully used to determine the critical properties of these nonequilibrium phase transitions. In particular, in both cases, we obtain good estimates of the critical point and the dynamical critical exponent of the models. For directed bond percolation we are, furthermore, able to extract critical exponents associated with the correlation length and the order parameter. We discuss the relation of our analysis with low-rank approximations of datasets.