PreprintCC BY 4.0arXiv
Sampling the XY model with an attention-based neural network
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 96×96, 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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BibTeX
@misc{bialas2026sampling,
title = {{Sampling the XY model with an attention-based neural network}},
author = {Piotr Białas and Christian D. Morales and Tomasz Stebel and Dawid Zapolski},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.23783},
eprint = {2610.23783},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.23783},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Sampling the XY model with an attention-based neural network
AU - Piotr Białas
AU - Christian D. Morales
AU - Tomasz Stebel
AU - Dawid Zapolski
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.23783
UR - https://arxiv.org/abs/2610.23783
AB - 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 96×96, 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.
ER -