README.md

metadata

license: cc-by-4.0
tags:
  - physics
  - lattice-field-theory
  - monte-carlo
  - phase-transition
pretty_name: 2D phi^4 lattice field configurations
size_categories:
  - 10K<n<100K

2D φ⁴ lattice field configurations

Monte Carlo configurations of the two-dimensional scalar φ⁴ theory on periodic square lattices, generated for training and benchmarking generative models (score-based diffusion), and for unsupervised-learning studies of the phase transition (PCA).

Physics

Lattice action in the hopping-parameter form

$$S[\varphi ]=\sum _x[-2\kappa \sum _{\mu =1,2}{\varphi }_x{\varphi }_{x+\widehat{\mu }}+(1-2\lambda ){\varphi }_x^2+\lambda {\varphi }_x^4]S[\backslash phi]\; =\; \backslash sum\_x\; \backslash Big[\; -2\backslash kappa\; \backslash sum\_\{\backslash mu=1,2\}\; \backslash phi\_x\; \backslash phi\_\{x+\backslash hat\backslash mu\}\; +\; (1-2\backslash lambda)\backslash phi\_x^2\; +\; \backslash lambda\; \backslash phi\_x^4\; \backslash Big]$$

with quartic coupling fixed at λ = 0.022. The three hopping parameters straddle the phase transition (κ_c ≈ 0.2708 for this λ):

κ	phase
0.26	symmetric (disordered)
0.2705	near-critical
0.28	broken (ordered)

Files

15 .npz files, one per (κ, L) pair:

cfgs_wolff_fahmc_k=<kappa>_l=0.022_<L>^2.npz,  L ∈ {8, 16, 32, 64, 128}

Each file contains 10240 independent configurations. Keys:

key	content
cfgs	float64 array, shape (10240, L, L)
κ, λ	hopping parameter, quartic coupling
N, n_samples	lattice size L, number of configurations
acc_rate	HMC acceptance rate
ε_final	final tuned HMC step size

Total size ≈ 5 GB (the L=128 files are 1.3 GB each).

Generation

Sampled with alternating Wolff cluster updates and Fourier-accelerated HMC (wolff_fahmc), which keeps autocorrelations short even near criticality. Configurations within a file are saved after thermalization and thinned so they are effectively independent.

Usage

import numpy as np

d = np.load("cfgs_wolff_fahmc_k=0.2705_l=0.022_32^2.npz")
phi = d["cfgs"]            # (10240, 32, 32)
M = phi.mean(axis=(1, 2))  # per-configuration magnetization

pca_phi4.py reproduces the PCA analysis figures (pca_phi4_L32.png, pca_phi4_L128.png): the PCA spectrum equals the sorted momentum-space propagator G(k) = ⟨|φ(k)|²⟩, PC1 = L·M is the magnetization mode, and PC2–PC5 span the lowest-momentum plane-wave quadruplet.