Sampling the XY model with an attention-based neural network
cond-mat.dis-nn, cond-mat.stat-mech, cs.LG, hep-lat
Submitted: 2026-10-16
Updated: 2026-10-16
Comments: 19 pages, 6 figures
License: http://creativecommons.org/licenses/by/4.0/
The gist: 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
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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