Learning Degenerate Manifolds of Frustrated Magnets with Boltzmann Machines
This provides a generative framework for physicists studying disordered magnetic phases, though it is incremental as it applies existing RBMs to new data in this domain.
The paper tackled modeling spin configurations in frustrated magnets using Restricted Boltzmann Machines (RBMs), demonstrating that RBMs accurately learn degenerate manifolds, such as reproducing oscillatory correlations in the ANNNI model and matching Monte Carlo simulations in kagome spin ice with close correlation functions.
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.