Sampling the XY model with an attention-based neural network

Piotr Białas; Christian D. Morales; Tomasz Stebel; Dawid Zapolski

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arXiv · 2610.23783

Sampling the XY model with an attention-based neural network

Piotr Białas·Christian D. Morales·Tomasz Stebel·Dawid Zapolski

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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.

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Piotr Białas, Christian D. Morales, Tomasz Stebel, Dawid Zapolski. 2026-10-16. Sampling the XY model with an attention-based neural network. https://arxiv.org/abs/2610.23783

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