Sampling the XY model with an attention-based neural network
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.
| Authors | Piotr Białas, Christian D. Morales, Tomasz Stebel et al. |
|---|---|
| Primary category | cond-mat.dis-nn |
| Published | 16 October 2026 |
| Last updated at source | 16 October 2026 |
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