README.md

metadata

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, 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)