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[2511.19879] Learning Degenerate Manifolds of Frustrated Magnets with Boltzmann Machines
Summary
This paper explores the use of Restricted Boltzmann Machines (RBMs) to model spin configurations in frustrated magnets, demonstrating their effectiveness in learning complex magnetic states.
Why It Matters
Understanding frustrated magnets is crucial for advancing materials science and condensed matter physics. This research highlights the potential of machine learning techniques, specifically RBMs, to model complex systems, which can lead to new insights in both theoretical and applied physics.
Key Takeaways
- RBMs can effectively model spin configurations in frustrated magnets.
- The study showcases RBMs' ability to learn ground-state manifolds in complex magnetic systems.
- Correlation functions from RBM-generated data align closely with Monte Carlo simulations.
- Uniform-sign bias fields in RBMs are necessary for accurate modeling of certain magnetic phases.
- This research opens avenues for applying machine learning in materials science.
Condensed Matter > Strongly Correlated Electrons arXiv:2511.19879 (cond-mat) [Submitted on 25 Nov 2025 (v1), last revised 18 Feb 2026 (this version, v2)] Title:Learning Degenerate Manifolds of Frustrated Magnets with Boltzmann Machines Authors:Ho Jang, Jackson C. Glass, Gia-Wei Chern View a PDF of the paper titled Learning Degenerate Manifolds of Frustrated Magnets with Boltzmann Machines, by Ho Jang and 1 other authors View PDF HTML (experimental) Abstract:We show that Restricted Boltzmann Machines (RBMs) provide a flexible generative framework for modeling spin configurations in disordered yet strongly correlated phases of frustrated magnets. As a benchmark, we first demonstrate that an RBM can learn the zero-temperature ground-state manifold of the one-dimensional ANNNI model at its multiphase point, accurately reproducing its characteristic oscillatory and exponentially decaying correlations. We then apply RBMs to kagome spin ice and show that they successfully learn the local ice rules and short-range correlations of the extensively degenerate ice-I manifold. Correlation functions computed from RBM-generated configurations closely match those from direct Monte Carlo simulations. For the partially ordered ice-II phase -- featuring long-range charge order and broken time-reversal symmetry -- accurate modeling requires RBMs with uniform-sign bias fields, mirroring the underlying symmetry breaking. These results highlight the utility of RBMs as generative models for learn...