Overcoming critical slowing down in frustrated spin systems by learned multiscale sampling
Abstract
Cluster algorithms, such as the Swendsen--Wang and Wolff methods, are among the most successful MCMC methods for mitigating critical slowing down in statistical systems. These constructive cluster algorithms, however, fail in the presence of even extremely weak frustration. Here, we sidestep this fundamental limitation by learning rather than constructing the relevant clusters. Specifically, we use the wavelet conditional renormalization group (WCRG) sampling method to learn the probability distribution of collective fluctuations of a frustrated two-dimensional soft-spin model. Configurations are then generated recursively from coarse to fine scales by sampling conditional wavelet distributions. The WCRG method reproduces the main statistical properties of the system across different phases, including the local-field distribution and the structure factor. At an Ising-like critical point, the conditional dynamics remains decorrelated within 𝒪(1) sweeps at each scale, yielding an overall sampling complexity of 𝒪(log2 L), thus making WCRG much more efficient than standard local MCMC methods. These results show that learned multiscale sampling can overcome critical slowing down in frustrated systems for which conventional cluster algorithms fail. By assessing the sampling accuracy of different observables, we also clarify the main tradeoff of the WCRG method: the accuracy of the fast sampling scheme depends on the expressiveness of the energy-based model used to estimate the wavelet conditional distributions.
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BibTeX
@misc{bandini2026overcoming,
title = {{Overcoming critical slowing down in frustrated spin systems by learned multiscale sampling}},
author = {Gabriele Bandini and Giulio Biroli and Patrick Charbonneau and Andrea Gambassi},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.31114},
eprint = {2608.31114},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.31114},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Overcoming critical slowing down in frustrated spin systems by learned multiscale sampling
AU - Gabriele Bandini
AU - Giulio Biroli
AU - Patrick Charbonneau
AU - Andrea Gambassi
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.31114
UR - https://arxiv.org/abs/2608.31114
AB - Cluster algorithms, such as the Swendsen--Wang and Wolff methods, are among the most successful MCMC methods for mitigating critical slowing down in statistical systems. These constructive cluster algorithms, however, fail in the presence of even extremely weak frustration. Here, we sidestep this fundamental limitation by learning rather than constructing the relevant clusters. Specifically, we use the wavelet conditional renormalization group (WCRG) sampling method to learn the probability distribution of collective fluctuations of a frustrated two-dimensional soft-spin model. Configurations are then generated recursively from coarse to fine scales by sampling conditional wavelet distributions. The WCRG method reproduces the main statistical properties of the system across different phases, including the local-field distribution and the structure factor. At an Ising-like critical point, the conditional dynamics remains decorrelated within 𝒪(1) sweeps at each scale, yielding an overall sampling complexity of 𝒪(log_2 L), thus making WCRG much more efficient than standard local MCMC methods. These results show that learned multiscale sampling can overcome critical slowing down in frustrated systems for which conventional cluster algorithms fail. By assessing the sampling accuracy of different observables, we also clarify the main tradeoff of the WCRG method: the accuracy of the fast sampling scheme depends on the expressiveness of the energy-based model used to estimate the wavelet conditional distributions.
ER -