Detecting Phase Transitions from Data Using Generative Learning.

Identifying phase transitions in complex many-body systems traditionally necessitates the definition of specific order parameters, a task often requiring prior knowledge of the statistical model and the symmetry-breaking mechanism. In this work, we propose a framework for detecting phase transitions directly from raw (experimental) data without requiring knowledge of the underlying model Hamiltonian, parameters, or pre-defined labels. Inspired by generative modeling in machine learning, our method utilizes autoregressive networks to estimate the normalized probability distribution of the system from raw configuration data. We then quantify the intrinsic sensitivity of this learned distribution to control parameters (such as temperature) to construct a robust indicator of phase transitions. This indicator is based on the expectation of the change in absolute logarithmic probability, derived entirely from the raw data. Our approach is purely data-driven: it takes raw data across varying control parameters as input and outputs the most likely estimate of the phase transition point. To validate our approach, we conduct extensive numerical experiments on the 2D Ising model on both triangular and square lattices, and on the Sherrington-Kirkpatrick (SK) model utilizing raw data generated via Markov Chain Monte Carlo and Tensor Network methods. The results demonstrate that our generative approach accurately identifies phase transitions using only raw data. Our framework provides a general tool for exploring critical phenomena in model systems, with the potential to be extended to realistic experimental data where theoretical descriptions remain incomplete.