arXiv:2511.19879v1 Announce Type: cross 
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 learning constrained and highly frustrated magnetic states.

أظهر الباحثون أن آلات بولتزمان المقيدة (RBMs) يمكن أن تُستخدم بفعالية لنمذجة تكوينات الدوران في المغناطيسات المحبطة، مع التركيز على قدرتها على تعلم مجموعة الحالة الأرضية عند درجة حرارة صفر من نموذج ANNNI أحادي الأبعاد وقواعد الجليد المحلية لجليد الكاجومي. تعيد RBMs إنتاج دوال الارتباط بدقة، مما يتماشى بشكل وثيق مع نتائج محاكاة مونت كارلو.

Investigadores han demostrado que las Máquinas de Boltzmann Restringidas (RBM) pueden modelar eficazmente las configuraciones de espín en imanes frustrados, destacando su capacidad para aprender el manifold del estado fundamental a temperatura cero del modelo ANNNI unidimensional y las reglas locales de hielo del hielo de kagome. Las RBM reproducen con precisión las funciones de correlación, alineándose estrechamente con los resultados de simulaciones de Monte Carlo.

Des chercheurs ont démontré que les machines de Boltzmann restreintes (RBM) peuvent modéliser efficacement les configurations de spins dans des aimants frustrés, en mettant particulièrement en avant leur capacité à apprendre le manchon d'état fondamental à température nulle du modèle ANNNI unidimensionnel et les règles de glace locales de la glace de kagome. Les RBM reproduisent avec précision les fonctions de corrélation, s'alignant étroitement avec les résultats des simulations de Monte Carlo.

Researchers have demonstrated that Restricted Boltzmann Machines (RBMs) can effectively model spin configurations in frustrated magnets, particularly showcasing their ability to learn the zero-temperature ground-state manifold of the one-dimensional ANNNI model and the local ice rules of kagome spin ice. The RBMs accurately reproduce correlation functions, aligning closely with results from Monte Carlo simulations.

Learning Degenerate Manifolds of Frustrated Magnets with Boltzmann Machines

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