An $O(\log N)$ Monte Carlo method for periodic Coulomb systems
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911375116206080 |
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| author | Gao, Xuanzhao Jiang, Shidong Liang, Jiuyang Zhou, Qi |
| author_facet | Gao, Xuanzhao Jiang, Shidong Liang, Jiuyang Zhou, Qi |
| contents | Efficient Monte Carlo (MC) sampling of many-body systems with long-range electrostatics is often limited by the cost of per-move energy-difference evaluation under periodic boundary conditions. We present DMK-MC, an accelerated MC method that adapts the dual-space multilevel kernel-splitting (DMK) framework to single-particle Metropolis updates. DMK-MC computes the energy change and, upon acceptance, updates the stored incoming plane-wave fields with $O(1)$ work per tree level, yielding an overall $O(\log N)$ expected work per trial move for fixed accuracy. The method decomposes the Coulomb kernel into three components: a global, periodized smooth part; a multilevel sequence of smooth difference kernels whose interactions are restricted to same-level colleague boxes; and a singular residual kernel whose short-range interactions are evaluated directly. Benchmarks on uniform, highly nonuniform, and implicit-solvent electrolyte and colloidal configurations show that DMK-MC consistently outperforms a recent FMM-based $O(\log N)$ Monte Carlo method, delivering several-fold speedups at comparable tolerances. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_09288 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An $O(\log N)$ Monte Carlo method for periodic Coulomb systems Gao, Xuanzhao Jiang, Shidong Liang, Jiuyang Zhou, Qi Computational Physics 82B80, 65Y20, 65E05, 68W25, 70F10 Efficient Monte Carlo (MC) sampling of many-body systems with long-range electrostatics is often limited by the cost of per-move energy-difference evaluation under periodic boundary conditions. We present DMK-MC, an accelerated MC method that adapts the dual-space multilevel kernel-splitting (DMK) framework to single-particle Metropolis updates. DMK-MC computes the energy change and, upon acceptance, updates the stored incoming plane-wave fields with $O(1)$ work per tree level, yielding an overall $O(\log N)$ expected work per trial move for fixed accuracy. The method decomposes the Coulomb kernel into three components: a global, periodized smooth part; a multilevel sequence of smooth difference kernels whose interactions are restricted to same-level colleague boxes; and a singular residual kernel whose short-range interactions are evaluated directly. Benchmarks on uniform, highly nonuniform, and implicit-solvent electrolyte and colloidal configurations show that DMK-MC consistently outperforms a recent FMM-based $O(\log N)$ Monte Carlo method, delivering several-fold speedups at comparable tolerances. |
| title | An $O(\log N)$ Monte Carlo method for periodic Coulomb systems |
| topic | Computational Physics 82B80, 65Y20, 65E05, 68W25, 70F10 |
| url | https://arxiv.org/abs/2601.09288 |