# Learning Degenerate Manifolds of Frustrated Magnets with Boltzmann Machines

arXiv: https://arxiv.org/abs/2511.19879 · HTML: https://mlsanity.com/paper/2511.19879/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 86 references that are in the map.
- First posted on arXiv 25 Nov 2025.

## Builds on (most cited first, 18 of 18)

- [Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics](https://mlsanity.com/paper/1707.09571/) (2017)
- [Machine Learning Force Fields](https://mlsanity.com/paper/2010.07067/) (2020)
- [Machine Learning in the Search for New Fundamental Physics](https://mlsanity.com/paper/2112.03769/) (2021)
- [Restricted Boltzmann Machine, recent advances and mean-field theory](https://mlsanity.com/paper/2011.11307/) (2020)
- [Machine Learning for Condensed Matter Physics](https://mlsanity.com/paper/2005.14228/) (2020)
- [Accelerate Monte Carlo Simulations with Restricted Boltzmann Machines](https://mlsanity.com/paper/1610.02746/) (2016)
- [Machine learning dynamics of phase separation in correlated electron magnets](https://mlsanity.com/paper/2006.04205/) (2020)
- [Anomalous phase separation dynamics in a correlated electron system: machine-learning enabled large-scale kinetic Monte Carlo simulations](https://mlsanity.com/paper/2105.13304/) (2021)
- [Machine learning electron correlation in a disordered medium](https://mlsanity.com/paper/1810.02323/) (2018)
- [Machine learning nonequilibrium electron forces for adiabatic spin dynamics](https://mlsanity.com/paper/2112.12124/) (2021)
- [Learning Thermodynamics with Boltzmann Machines](https://mlsanity.com/paper/1606.02718/) (2016)
- [Descriptors for Machine Learning Model of Generalized Force Field in Condensed Matter Systems](https://mlsanity.com/paper/2201.00798/) (2022)
- [Machine learning for phase ordering dynamics of charge density waves](https://mlsanity.com/paper/2303.03493/) (2023)
- [Machine learning predictions for local electronic properties of disordered correlated electron systems](https://mlsanity.com/paper/2204.05967/) (2022)
- [Deep Learning the Ising Model Near Criticality](https://mlsanity.com/paper/1708.04622/) (2017)
- [Coarsening of chiral domains in itinerant electron magnets: A machine learning force field approach](https://mlsanity.com/paper/2403.11705/) (2024)
- [Kinetics of orbital ordering in cooperative Jahn-Teller models: Machine-learning enabled large-scale simulations](https://mlsanity.com/paper/2405.14776/) (2024)
- [The Accuracy of Restricted Boltzmann Machine Models of Ising Systems](https://mlsanity.com/paper/2004.12867/) (2020)

## Abstract (arXiv)

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 learning constrained and highly frustrated magnetic states.