# Unveiling phase transitions with machine learning

arXiv: https://arxiv.org/abs/1904.01486 · HTML: https://mlsanity.com/paper/1904.01486/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Apr 2019.

## Built on by (most cited first, 7 of 7)

- [Hessian Geometry of Latent Space in Generative Models](https://mlsanity.com/paper/2506.10632/) (2025)
- [Exponentially improved efficient machine learning for quantum many-body states with provable guarantees](https://mlsanity.com/paper/2304.04353/) (2023)
- [A simple framework for contrastive learning phases of matter](https://mlsanity.com/paper/2205.05607/) (2022)
- [Can a CNN trained on the Ising model detect the phase transition of the q-state Potts model?](https://mlsanity.com/paper/2104.03632/) (2021)
- [Quantitative analysis of phase transitions in two-dimensional XY models using persistent homology](https://mlsanity.com/paper/2109.10960/) (2021)
- [Counting Phases and Faces Using Bayesian Thermodynamic Integration](https://mlsanity.com/paper/2206.07494/) (2022)
- [Quantum neural networks facilitating quantum state classification](https://mlsanity.com/paper/2504.06622/) (2025)

## Abstract (arXiv)

The classification of phase transitions is a central and challenging task in condensed matter physics. Typically, it relies on the identification of order parameters and the analysis of singularities in the free energy and its derivatives. Here, we propose an alternative framework to identify quantum phase transitions, employing both unsupervised and supervised machine learning techniques. Using the axial next-nearest neighbor Ising (ANNNI) model as a benchmark, we show how unsupervised learning can detect three phases (ferromagnetic, paramagnetic, and a cluster of the antiphase with the floating phase) as well as two distinct regions within the paramagnetic phase. Employing supervised learning we show that transfer learning becomes possible: a machine trained only with nearest-neighbour interactions can learn to identify a new type of phase occurring when next-nearest-neighbour interactions are introduced. All our results rely on few and low dimensional input data (up to twelve lattice sites), thus providing a computational friendly and general framework for the study of phase transitions in many-body systems.