AI Discovers Phase Transitions with 0.01% Accuracy

Researchers are developing increasingly sophisticated methods to identify phase transitions, crucial phenomena governing material behaviour, and a new study led by Brandon Yee, Wilson Collins and Maximilian Rutkowski, all from the Physics Lab, Yee Collins Research Group, details a significant advance in this field. Their work extends the Prometheus framework, enabling unsupervised discovery of phase transitions not only in two-dimensional classical systems, but also in three dimensions and, crucially, into the realm of quantum mechanics. This collaborative effort demonstrates the ability to accurately pinpoint critical temperatures and extract exponents for the 3D Ising model, and to detect exotic criticality in disordered quantum systems, achieving up to 2% accuracy in critical point detection. By systematically validating their approach across diverse physical domains, the team establishes a robust and generalisable tool for exploring complex phase diagrams where analytical solutions remain elusive, opening new avenues for materials discovery and fundamental physics research. A powerful new technique for finding hidden changes in complex systems, from magnetism to quantum materials, has been developed by scientists. The method automatically identifies critical points, moments where a material’s behaviour fundamentally alters, without needing prior knowledge of the physics involved, offering a route to understanding previously inaccessible phenomena and accelerating materials discovery. Researchers have extended a machine learning framework, named Prometheus, to identify phase transitions not only in complex three-dimensional classical systems but also in quantum materials. This addresses a long-standing challenge in condensed matter physics: discovering and characterising transitions without relying on prior knowledge or analytical solutions. Previous approaches often required pre-labelled data or manual intervention, limiting their ability to uncover genuinely new phenomena. Now, researchers demonstrate that a variational autoencoder (VAE) can autonomously pinpoint critical temperatures and extract key properties like critical exponents, even when exact solutions are unavailable. For the well-studied 3D Ising model, the framework accurately determined the critical temperature to within 0.01% of established values, alongside extracting critical exponents with over 70% accuracy. Statistical analysis confirmed correct identification of the system’s universality class, a categorization based on shared characteristics, without any prior analytical guidance. Beyond classical systems, the team developed quantum-aware VAEs capable of handling the complex, wave-like nature of quantum mechanics. Applying this to the transverse field Ising model, they achieved 2% accuracy in detecting the quantum critical point and successfully identified the ground state magnetization as the defining order parameter. The most striking result came from studying a disordered version of the same quantum system, where the research revealed exotic infinite-randomness criticality. Here, the framework not only detected this unusual behaviour but also extracted a tunneling exponent consistent with theoretical predictions, demonstrating that unsupervised learning can discern qualitatively different types of critical behaviour, moving beyond locating transition points. Precise critical temperature and exponent identification in benchmark Ising systems For the 3D Ising model, the framework accurately detected the critical temperature to within 0.01% of established literature values. This precision signifies a substantial advancement in unsupervised phase transition discovery, particularly in systems where analytical solutions are unavailable. Furthermore, critical exponents were extracted with an accuracy ranging from 70 to 75%, correctly identifying the 3D Ising universality class without any prior analytical guidance. Applying a quantum-aware Variational Autoencoder (Q-VAE) to the transverse field Ising model yielded 2% accuracy in critical point detection. Beyond locating the transition, the research successfully discovered ground state magnetization as the order parameter, revealing the underlying physical mechanism driving the phase change. The most striking result emerged from studying the disordered transverse field Ising model, where the framework detected exotic infinite-randomness criticality. Here, the system extracted a tunneling exponent of 0.48 ±0.08, a value in remarkable agreement with the theoretical prediction of 0.5. This represents the first instance of unsupervised learning identifying qualitatively different types of critical behaviour, extending beyond the mere location of transition points. At a broader level, systematic validation across classical thermal transitions and quantum phase transitions establishes that VAE-based discovery generalizes across fundamentally different physical domains. Instead of relying on pre-existing knowledge, the framework consistently delivers precise results, providing practical tools for exploring complex phase diagrams, including those found in frustrated magnets, quantum materials, and topological phases. Since analytical methods often fail in these domains, this unsupervised approach offers a valuable alternative for materials scientists and physicists, suggesting a pathway towards automated discovery in condensed matter physics and potentially accelerating the identification of new materials and phenomena. Variational autoencoders detect phase transitions using a 72-qubit superconducting processor A 72-qubit superconducting processor forms the foundation of the methodology for discovering phase transitions, extending the Prometheus framework from two-dimensional classical systems to three-dimensional classical and quantum scenarios. Initially, work focused on adapting the framework to handle the increased complexity of three-dimensional systems, a necessary step given the absence of analytical solutions for models like the 3D Ising model. This involved careful consideration of scalability, ensuring the system could efficiently process data in higher dimensions and accurately capture fluctuations inherent in these systems. The core of this adaptation relies on variational autoencoders (VAEs), a type of artificial neural network trained to compress and reconstruct data, thereby identifying key features indicative of phase transitions. Scaling up the 2D approach proved insufficient for quantum systems, demanding a fundamentally new architecture. Consequently, researchers developed Quantum-aware VAEs (Q-VAEs) designed to process complex-valued wavefunctions, the mathematical description of quantum states. These Q-VAEs incorporate a fidelity-based loss function, guiding the learning process towards physically meaningful latent representations. By employing this technique, the system can effectively learn the underlying structure of quantum phase transitions without prior knowledge of the order parameter. Validating the performance of these methods required rigorous testing across diverse physical systems, systematically applying the framework to both classical thermal transitions and quantum phase transitions, varying the strength of external fields. This broad validation strategy aimed to establish the generalizability of VAE-based discovery, demonstrating its potential to explore phase diagrams where analytical solutions are unavailable and providing tools for materials design and quantum computing. Once established, the framework’s ability to identify critical points and extract exponents was assessed against known values and theoretical predictions. Unsupervised machine learning identifies phase transitions and criticality without prior knowledge Pinpointing the precise moment when systems tip from one state to another remains a formidable challenge. For decades, identifying phase transitions relied heavily on pre-existing knowledge of a system’s underlying symmetries and expected behaviour. Now, a new framework, extending the Prometheus system, offers a genuinely unsupervised approach, successfully navigating these transitions in both classical and quantum realms without needing such prior assumptions. This isn’t merely about achieving higher accuracy in locating known critical points; it’s about opening up exploration in areas where the rules are unclear. Previously, detecting different types of criticality, the subtle distinctions between order parameters and scaling behaviours, demanded deep theoretical understanding. This work demonstrates that machine learning algorithms, specifically variational autoencoders, can autonomously classify these behaviours, even uncovering exotic infinite-randomness criticality previously characterised by complex theoretical calculations. Reliance on disorder averaging across numerous realisations, up to one hundred in their simulations, highlights a computational cost that may limit application to larger, more complex systems. The ability to learn phase diagrams directly from data promises to reshape materials discovery and condensed matter physics. However, the method’s current limitations should not be overlooked; the framework was tested on established models, and its performance on genuinely unknown systems remains to be seen. The convergence of unsupervised learning and physics suggests a future where algorithms not only identify transitions but also propose entirely new theoretical frameworks, potentially revealing hidden connections between seemingly disparate physical phenomena. Rather than replacing theoretical insight, these tools will likely augment it, accelerating the pace of scientific discovery in a field ripe for exploration. 👉 More information 🗞 From Classical to Quantum: Extending Prometheus for Unsupervised Discovery of Phase Transitions in Three Dimensions and Quantum Systems 🧠 ArXiv: https://arxiv.org/abs/2602.14928 Tags: