Preserving Hamiltonian Locality in Real-Space Coarse-Graining via Kernel Projection
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911533746880512 |
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| author | Haoyuan, Sun |
| author_facet | Haoyuan, Sun |
| contents | Numerical simulations of critical lattice systems are fundamentally limited by critical slowing down, as long-range correlations are typically established through slow temporal equilibration. A physically constrained generative framework that replaces temporal relaxation with a spatial projection mechanism for critical systems is proposed. Using the two-dimensional Ising model at criticality as a benchmark, we introduce an energy-constrained kernel that synthesizes large-scale configurations from compact equilibrated seeds by enforcing Hamiltonian-level observables. The generated configurations are projected onto the nearest-neighbor energy manifold, ensuring thermodynamic consistency while retaining universal critical properties. We show that the resulting configurations reproduce scale-invariant spin correlations, Binder cumulants, and isotropic structure factors for lattice sizes exceeding 10,000, without iterative Monte Carlo equilibration. While not a strict renormalization group transformation, and motivated by renormalization ideas, the method provides a practical inverse mapping that retains universal features of criticality and enables efficient GPU-parallel generation of ultra-large critical ensembles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_08502 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Preserving Hamiltonian Locality in Real-Space Coarse-Graining via Kernel Projection Haoyuan, Sun Statistical Mechanics Numerical simulations of critical lattice systems are fundamentally limited by critical slowing down, as long-range correlations are typically established through slow temporal equilibration. A physically constrained generative framework that replaces temporal relaxation with a spatial projection mechanism for critical systems is proposed. Using the two-dimensional Ising model at criticality as a benchmark, we introduce an energy-constrained kernel that synthesizes large-scale configurations from compact equilibrated seeds by enforcing Hamiltonian-level observables. The generated configurations are projected onto the nearest-neighbor energy manifold, ensuring thermodynamic consistency while retaining universal critical properties. We show that the resulting configurations reproduce scale-invariant spin correlations, Binder cumulants, and isotropic structure factors for lattice sizes exceeding 10,000, without iterative Monte Carlo equilibration. While not a strict renormalization group transformation, and motivated by renormalization ideas, the method provides a practical inverse mapping that retains universal features of criticality and enables efficient GPU-parallel generation of ultra-large critical ensembles. |
| title | Preserving Hamiltonian Locality in Real-Space Coarse-Graining via Kernel Projection |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2602.08502 |