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This study introduces a transformer-based variational autoregressive network designed to sample continuous lattice systems, specifically targeting the two-dimensional XY model near its critical transition point. By integrating physics-informed mechanisms like locality-aware attention, the architecture achieves superior sampling efficiency compared to traditional Markov Chain Monte Carlo methods while accurately reproducing key thermodynamic observables.
Sampling the XY model with an attention-based neural network
arXiv:2610.23783v1 Announce Type: cross Abstract: We present a transformer-based variational autoregressive network for sampling lattice systems with continuous degrees of freedom and apply it to the two-dimensional XY model near the Berezinskii-Kosterlitz-Thouless transition. The architecture is combined with physics-informed ingredients: locality-informed attention and approximate probabilities. The resulting sampler significantly outperforms existing neural samplers. We train the model on lattices up to $96\times96$, verify with a mode-dropping estimator that no parts of the configuration space are missed, and reproduce the energy, magnetization and helicity modulus obtained with the traditional Markov Chain Monte Carlo algorithm.
Abstract:We present a transformer-based variational autoregressive network for sampling lattice systems with continuous degrees of freedom and apply it to the two-dimensional XY model near the Berezinskii-Kosterlitz-Thouless transition. The architecture is combined with physics-informed ingredients: locality-informed attention and approximate probabilities. The resulting sampler significantly outperforms existing neural samplers. We train the model on lattices up to $96\times96$, verify with a mode-dropping estimator that no parts of the configuration space are missed, and reproduce the energy, magnetization and helicity modulus obtained with the traditional Markov Chain Monte Carlo algorithm.
Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech); Machine Learning (cs.LG); High Energy Physics - Lattice (hep-lat)
arXiv:2610.23783 [cond-mat.dis-nn]
(or arXiv:2610.23783v1 [cond-mat.dis-nn] for this version)
https://doi.org/10.48550/arXiv.2610.23783 arXiv-issued DOI via DataCite (pending registration)
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