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PreprintarXiv licencearXiv

Stochastic Path Sampler For Lattice Field Theory

  • Shiyang Chen1
  • Moxian Qian2,3
  • Gert Aarts A1
  • Biagio Lucini A4
  • Kai Zhou5,3
5 affiliations
  1. 1Centre for Quantum Fields and Gravity , Department of Physics , Swansea University , SA2 8PP , Swansea , United Kingdom
  2. 2Johannes Gutenberg University Mainz , 55128 Mainz , Germany
  3. 3School of Science and Engineering , The Chinese University of Hong Kong , Shenzhen (CUHK- Shenzhen) , Guangdong , 518172 , China
  4. 4School of Mathematical Sciences , Queen Mary University of London , Mile End Road , London , E1 4NS , UK
  5. 5School of Artificial Intelligence , The Chinese University of Hong Kong , Shenzhen (CUHK-Shen- zhen) , Guangdong , 518172 , China
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Abstract

In lattice field theory, target distributions are known only up to normalization, (\tildeπ(ϕ)\propto e^{-S(ϕ)}), while the partition function is intractable. Markov chain Monte Carlo simulations often become inefficient near phase transitions or the continuum limit due to critical slowing down. In this work, we propose a novel sampler based on nonequilibrium thermodynamics, called Stochastic Path Sampler (SPS), which can generate configurations for the unnormalized target distribution without requiring training data. The central idea of SPS is to establish a trajectory-level balance for learnable forward and backward stochastic dynamics between two equilibrium states, namely the prior and target distributions. This is achieved by minimizing the path-space variational free energy, equivalently an entropy-production upper bound, defined by the log-ratio of forward and auxiliary backward trajectory measures, thereby enhancing the reversibility of the forward and backward processes. The learned forward process provides independent proposals, which are subsequently corrected by an extended-space Independence Metropolis--Hastings step. In two-dimensional (ϕ^4) theory, we demonstrate that our neural sampler can achieve the same sampling quality as HMC but with a much shorter autocorrelation time in the critical region. This sampler offers a stochastic-quantization-inspired route to data-free proposal construction for lattice field theory by leveraging a variational free-energy principle derived from path-space irreversibility.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026stochastic,
  title = {{Stochastic Path Sampler For Lattice Field Theory}},
  author = {Shiyang Chen and Moxian Qian and Gert Aarts A and Biagio Lucini A and Kai Zhou},
  howpublished = {arXiv},
  year = {2026},
  month = jun,
  doi = {10.48550/arxiv.2606.13790},
  eprint = {2606.13790},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.13790},
}
RIS
TY  - UNPB
TI  - Stochastic Path Sampler For Lattice Field Theory
AU  - Shiyang Chen
AU  - Moxian Qian
AU  - Gert Aarts A
AU  - Biagio Lucini A
AU  - Kai Zhou
PY  - 2026
DA  - 2026/06/11
PB  - arXiv
DO  - 10.48550/arxiv.2606.13790
UR  - https://arxiv.org/abs/2606.13790
AB  - In lattice field theory, target distributions are known only up to normalization, (\tildeπ(ϕ)\propto e^{-S(ϕ)}), while the partition function is intractable. Markov chain Monte Carlo simulations often become inefficient near phase transitions or the continuum limit due to critical slowing down. In this work, we propose a novel sampler based on nonequilibrium thermodynamics, called Stochastic Path Sampler (SPS), which can generate configurations for the unnormalized target distribution without requiring training data. The central idea of SPS is to establish a trajectory-level balance for learnable forward and backward stochastic dynamics between two equilibrium states, namely the prior and target distributions. This is achieved by minimizing the path-space variational free energy, equivalently an entropy-production upper bound, defined by the log-ratio of forward and auxiliary backward trajectory measures, thereby enhancing the reversibility of the forward and backward processes. The learned forward process provides independent proposals, which are subsequently corrected by an extended-space Independence Metropolis--Hastings step. In two-dimensional (ϕ^4) theory, we demonstrate that our neural sampler can achieve the same sampling quality as HMC but with a much shorter autocorrelation time in the critical region. This sampler offers a stochastic-quantization-inspired route to data-free proposal construction for lattice field theory by leveraging a variational free-energy principle derived from path-space irreversibility.
SN  - 2331-8422
ER  -