| --- |
| license: mit |
| tags: |
| - lattice-field-theory |
| - diffusion-models |
| - physics |
| --- |
| |
| # 2D Yukawa model: HMC configurations + score-based diffusion model |
|
|
| Scalar-field sector of the 2D staggered Yukawa model from Albergo et al., |
| [arXiv:2106.05934](https://arxiv.org/abs/2106.05934), sampled with pseudofermion |
| HMC, plus a score-based diffusion model (VE-SDE, NCSN++-style 2D U-Net) trained |
| on the g=0.1 ensemble. |
|
|
| ## Physics setup |
|
|
| 16x16 lattice, two-flavor staggered fermions, m_f = 0. |
| |
| | set | m^2 | lambda | g | <\|M\|> (HMC) | |
| |---|---|---|---|---| |
| | g=0.1 | -4.00 | 6.0 | 0.1 | 0.07326(17) | |
| | g=0.3 | -1.55 | 2.4 | 0.3 | — | |
| |
| ## Contents |
| |
| - `YukawaFermionHMC2D.jl`, `generate_samples.jl`, `force_ratio.jl` — Julia |
| pseudofermion HMC (sparse Cholesky solves; paper Table II force-ratio checks) |
| - `samples/yukawa_g{0.1,0.3}_L16_1000000.jld2` — 100k scalar configs each |
| (key `configs`, shape `(100000, 16, 16)`; 1M trajectories, save_every=10), |
| plus `.npz` mirrors and per-trajectory |M| histories |
| - `diffusion/` — PyTorch training/sampling/analysis for the diffusion model |
| (`train_yukawa.py`, `sample_yukawa.py`, `analysis_observables.py`, |
| `plot_chi_hist.py`; network/SDE definitions live in the parent DM repo) |
| - `diffusion/runs/yukawa_L16_g0.1_ncsnpp/models/` — log-spaced checkpoints |
| (epochs 1–65, sigma=50, batch 256, lr 1e-3, bf16) |
| - `diffusion/runs/yukawa_L16_g0.1_ncsnpp/data/` — generated samples |
| (`(16, 16, N)` npy, physical field units) and comparison figures |
|
|
| ## Diffusion-model validation (epoch 49, EM 2000 steps, log schedule, N=10240) |
|
|
| | observable | HMC (N=100k) | diffusion model | |
| |---|---|---| |
| | <\|M\|> | 0.07326(17) | 0.07328(59) | |
| | chi = V(<M^2> - <\|M\|>^2) | 0.7469(36) | 0.759(14) | |
|
|
