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[2602.14928] From Classical to Quantum: Extending Prometheus for Unsupervised Discovery of Phase Transitions in Three Dimensions and Quantum Systems
Summary
This article presents an extension of the Prometheus framework for unsupervised discovery of phase transitions, applying it to both classical and quantum systems in three dimensions.
Why It Matters
Understanding phase transitions is crucial in physics, particularly in materials science and quantum mechanics. This research enhances the Prometheus framework's capabilities, enabling more accurate detection of critical points and behaviors in complex systems, which can lead to advancements in both theoretical and applied physics.
Key Takeaways
- The Prometheus framework has been successfully extended to 3D classical and quantum systems.
- Achieved high accuracy in detecting critical temperatures and extracting critical exponents in the 3D Ising model.
- Developed quantum-aware VAE architectures that improve detection of quantum critical points.
- Demonstrated the ability to identify qualitatively different critical behaviors using unsupervised learning.
- Validated the framework's effectiveness across various physical domains, highlighting its robustness.
Condensed Matter > Disordered Systems and Neural Networks arXiv:2602.14928 (cond-mat) [Submitted on 16 Feb 2026] Title:From Classical to Quantum: Extending Prometheus for Unsupervised Discovery of Phase Transitions in Three Dimensions and Quantum Systems Authors:Brandon Yee, Wilson Collins, Maximilian Rutkowski View a PDF of the paper titled From Classical to Quantum: Extending Prometheus for Unsupervised Discovery of Phase Transitions in Three Dimensions and Quantum Systems, by Brandon Yee and 2 other authors View PDF HTML (experimental) Abstract:We extend the Prometheus framework for unsupervised phase transition discovery from 2D classical systems to 3D classical and quantum many-body systems, addressing scalability in higher dimensions and generalization to quantum fluctuations. For the 3D Ising model ($L \leq 32$), the framework detects the critical temperature within 0.01\% of literature values ($T_c/J = 4.511 \pm 0.005$) and extracts critical exponents with $\geq 70\%$ accuracy ($\beta = 0.328 \pm 0.015$, $\gamma = 1.24 \pm 0.06$, $\nu = 0.632 \pm 0.025$), correctly identifying the 3D Ising universality class via $\chi^2$ comparison ($p = 0.72$) without analytical guidance. For quantum systems, we developed quantum-aware VAE (Q-VAE) architectures using complex-valued wavefunctions and fidelity-based loss. Applied to the transverse field Ising model, we achieve 2\% accuracy in quantum critical point detection ($h_c/J = 1.00 \pm 0.02$) and successfully discover ground...
