Datasets:

phi4-generative
/

phi4-critical-configs

@@ -11,144 +11,93 @@ size_categories:
 - 10K<n<100K
 ---
-# φ⁴ lattice field configurations near the critical point
-Monte Carlo configurations of the scalar φ⁴ theory on periodic lattices close to the
-critical point, as plain NumPy `.npy` arrays.
-| | κ | λ | L | configurations per L | size |
-|---|---|---|---|---|---|
-| 2D | 0.2705 | 0.022 | 16, 32, 64, 128 | 10240 | 1.8 GB |
-| 3D | 0.1923 | 0.9 | 16, 32, 64, 128 | 2560 | 49 GB |
-## Physics
-Lattice action in hopping-parameter form
 $$S[\phi] = \sum_x \Big[-2\kappa \sum_{\mu=1}^{D} \phi_x \phi_{x+\hat\mu} + (1-2\lambda)\phi_x^2 + \lambda\phi_x^4\Big]$$
-on an L^D lattice with periodic boundary conditions and Boltzmann weight exp(−S).
-In 2D the quartic coupling is λ = 0.022 and the hopping parameter κ = 0.2705. For
-this λ the critical point is κ_c ≈ 0.27088 (Binder-cumulant estimate at L = 128,
-where U₄ reaches the 2D Ising value 0.6106), so κ = 0.2705 lies slightly on the
-symmetric side of κ_c and U₄ decreases with L.
-In 3D the couplings are λ = 0.9 and κ = 0.1923. The critical point for this λ is
-κ_c ≈ 0.19225 (Binder-cumulant crossing at L = 64), so κ = 0.1923 lies very slightly
-on the ordered side of κ_c and U₄ grows with L. At L = 16 and 32 it is within errors
-of the 3D Ising value 0.465.
-Both sets are therefore near-critical rather than exactly critical. The Binder
-cumulants in the tables below show how far each L is from the fixed point.
 ## Files
 ```
-README.md
-2D/phi4_2D_L16_kappa0.2705_lambda0.022.npy     shape (10240, 16, 16)          21 MB
-2D/phi4_2D_L32_kappa0.2705_lambda0.022.npy     shape (10240, 32, 32)          84 MB
-2D/phi4_2D_L64_kappa0.2705_lambda0.022.npy     shape (10240, 64, 64)         336 MB
-2D/phi4_2D_L128_kappa0.2705_lambda0.022.npy    shape (10240, 128, 128)      1342 MB
-3D/phi4_3D_L16_kappa0.1923_lambda0.9.npy       shape (2560, 16, 16, 16)       84 MB
-3D/phi4_3D_L32_kappa0.1923_lambda0.9.npy       shape (2560, 32, 32, 32)      671 MB
-3D/phi4_3D_L64_kappa0.1923_lambda0.9.npy       shape (2560, 64, 64, 64)     5369 MB
-3D/phi4_3D_L128_kappa0.1923_lambda0.9.npy      shape (2560, 128, 128, 128) 42950 MB
 ```
-Every array is float64 with shape (n_cfg, L, …, L). Axis 0 is the Markov-chain order
-of the sampler. The remaining axes are the lattice directions, all periodic. The
-values are the raw field φ_x with no normalisation applied.
-The configurations were generated by Monte Carlo sampling with Wolff cluster updates
-combined with Fourier-accelerated HMC. Each chain started from a random field and ran
-2000 warm-up iterations before production. In 2D every fifth production iteration was
-stored, in 3D every tenth. The 3D L = 128 file holds ten independent chains of 256
-configurations each, concatenated along axis 0 (entries 0 to 255 are chain 1, 256 to
-511 chain 2, and so on). All other files are single chains.
 ## Download
-Install the Hugging Face Hub client and fetch the whole dataset or a part of it. The
-3D L = 128 file alone is 43 GB, so pick what you need.
 ```bash
 pip install -U huggingface_hub
-# everything (51 GB) into ./phi4-critical-configs
-hf download YangyangTan/phi4-critical-configs --repo-type dataset --local-dir phi4-critical-configs
-# 2D only (1.8 GB)
-hf download YangyangTan/phi4-critical-configs --repo-type dataset --local-dir phi4-critical-configs --include "2D/*"
-# one lattice size only
-hf download YangyangTan/phi4-critical-configs --repo-type dataset --local-dir phi4-critical-configs --include "3D/*L64*"
 ```
-With huggingface_hub older than 1.0 the command is `huggingface-cli download` with
-the same arguments. The same from Python
 ```python
-from huggingface_hub import snapshot_download, hf_hub_download
-# 2D only
-path = snapshot_download("YangyangTan/phi4-critical-configs", repo_type="dataset",
-                         local_dir="phi4-critical-configs", allow_patterns=["2D/*"])
-# one file, returns its local path
-f = hf_hub_download("YangyangTan/phi4-critical-configs",
                     "3D/phi4_3D_L32_kappa0.1923_lambda0.9.npy", repo_type="dataset")
 ```
-If the dataset is private you must be logged in to an account that can see it. Run
-`hf auth login` once with a read token, or pass `token="hf_..."` to the Python calls.
-## Usage
-```python
-import numpy as np
-phi = np.load("phi4-critical-configs/2D/phi4_2D_L32_kappa0.2705_lambda0.022.npy")  # (10240, 32, 32)
-M = phi.mean(axis=(1, 2))                                                           # magnetisation per configuration
-phi3 = np.load("phi4-critical-configs/3D/phi4_3D_L64_kappa0.1923_lambda0.9.npy", mmap_mode="r")  # (2560, 64, 64, 64)
-```
-`np.load(path, mmap_mode="r")` reads the large files lazily.
-## Observables
-Computed from the files as stored, with M = L⁻ᴰ Σ_x φ_x,
-χ = Lᴰ (⟨M²⟩ − ⟨|M|⟩²) and U₄ = 1 − ⟨M⁴⟩ / (3⟨M²⟩²). Errors are jackknife over 64
-blocks of consecutive configurations. τ_int is the integrated autocorrelation time
-along axis 0 in units of stored configurations (Sokal window), measured for |M| and
-for the action S. A value of 0.5 means consecutive configurations are uncorrelated.
 2D, κ = 0.2705, λ = 0.022
-| L | ⟨\|M\|⟩ | χ | U₄ | τ_int(\|M\|) | τ_int(S) |
-|---|---|---|---|---|---|
-| 16 | 0.8149(26) | 23.0(3) | 0.5524(18) | 0.53 | 0.56 |
-| 32 | 0.7147(25) | 64.3(8) | 0.5672(16) | 0.58 | 0.60 |
-| 64 | 0.6019(26) | 212(3) | 0.5551(20) | 0.64 | 0.66 |
-| 128 | 0.4447(23) | 772(7) | 0.4815(27) | 0.69 | 0.79 |
 3D, κ = 0.1923, λ = 0.9
-| L | ⟨\|M\|⟩ | χ | U₄ | τ_int(\|M\|) | τ_int(S) |
-|---|---|---|---|---|---|
-| 16 | 0.2119(24) | 43.4(9) | 0.468(7) | 0.60 | 0.55 |
-| 32 | 0.1497(14) | 172(4) | 0.472(6) | 0.53 | 0.54 |
-| 64 | 0.1125(12) | 641(15) | 0.503(5) | 0.78 | 0.88 |
-| 128 | 0.0973(9) | 2372(73) | 0.566(4) | 0.74 | 0.74 |
-The stored configurations are close to statistically independent in every file. The
-largest value, τ_int = 0.88 for S in 3D at L = 64, corresponds to an effective
-sample size of about 2560 / (2 τ_int) ≈ 1450.
-## Related
-An earlier, independent set of 2D κ = 0.2705 chains (not thinned, so neighbouring
-configurations are correlated at L = 128), together with κ = 0.26 and κ = 0.28 and
-L = 8, is available in `.npz` form at
-https://huggingface.co/datasets/phi4-generative/2d-phi4-configs.

 - 10K<n<100K
 ---
+# φ⁴ lattice configurations near the critical point
+Monte Carlo configurations of the scalar φ⁴ theory on periodic lattices of volume V = L^D with action
 $$S[\phi] = \sum_x \Big[-2\kappa \sum_{\mu=1}^{D} \phi_x \phi_{x+\hat\mu} + (1-2\lambda)\phi_x^2 + \lambda\phi_x^4\Big]$$
+| D | κ | λ | κ_c | L | configurations per L | total size |
+|---|---|---|---|---|---|---|
+| 2 | 0.2705 | 0.022 | 0.27088 | 16, 32, 64, 128 | 10240 | 1.8 GB |
+| 3 | 0.1923 | 0.9 | 0.19225 | 16, 32, 64, 128 | 2560 | 49 GB |
+κ_c is the critical point estimated from the Binder cumulant.
 ## Files
 ```
+2D/phi4_2D_L16_kappa0.2705_lambda0.022.npy     (10240, 16, 16)            21 MB
+2D/phi4_2D_L32_kappa0.2705_lambda0.022.npy     (10240, 32, 32)            84 MB
+2D/phi4_2D_L64_kappa0.2705_lambda0.022.npy     (10240, 64, 64)           336 MB
+2D/phi4_2D_L128_kappa0.2705_lambda0.022.npy    (10240, 128, 128)        1342 MB
+3D/phi4_3D_L16_kappa0.1923_lambda0.9.npy       (2560, 16, 16, 16)         84 MB
+3D/phi4_3D_L32_kappa0.1923_lambda0.9.npy       (2560, 32, 32, 32)        671 MB
+3D/phi4_3D_L64_kappa0.1923_lambda0.9.npy       (2560, 64, 64, 64)       5369 MB
+3D/phi4_3D_L128_kappa0.1923_lambda0.9.npy      (2560, 128, 128, 128)   42950 MB
 ```
+Each array holds the float64 field values φ_x. Axis 0 runs over configurations in
+Monte Carlo order and the remaining axes are the periodic lattice directions. The
+configurations were generated with Wolff cluster updates combined with
+Fourier-accelerated HMC. The 3D L = 128 file consists of ten independent chains of
+256 configurations, concatenated along axis 0.
 ## Download
 ```bash
 pip install -U huggingface_hub
+# everything, 51 GB
+hf download phi4-generative/phi4-critical-configs --repo-type dataset --local-dir phi4-critical-configs
+# 2D only, 1.8 GB
+hf download phi4-generative/phi4-critical-configs --repo-type dataset --local-dir phi4-critical-configs --include "2D/*"
+# a single file
+hf download phi4-generative/phi4-critical-configs --repo-type dataset --local-dir phi4-critical-configs --include "3D/*L64*"
 ```
 ```python
+import numpy as np
+from huggingface_hub import hf_hub_download
+f = hf_hub_download("phi4-generative/phi4-critical-configs",
                     "3D/phi4_3D_L32_kappa0.1923_lambda0.9.npy", repo_type="dataset")
+phi = np.load(f, mmap_mode="r")    # (2560, 32, 32, 32)
+M = phi.mean(axis=(1, 2, 3))       # magnetisation per configuration
 ```
+## Physical quantities
+$$M = \frac{1}{V}\sum_x \phi_x, \qquad \chi = V\langle M^2\rangle, \qquad U_4 = 1-\frac{\langle M^4\rangle}{3\langle M^2\rangle^2}, \qquad \xi_2 = \frac{\sqrt{\chi/F-1}}{2\sin(\pi/L)}$$
+$$F = \frac{1}{V}\Big\langle\Big|\sum_x e^{2\pi i x_\mu/L}\phi_x\Big|^2\Big\rangle$$
+F is the propagator at the smallest nonzero momentum, averaged over the D directions
+μ, and ⟨S⟩/V is the action per site. Errors are jackknife over 64 blocks of
+consecutive configurations. The integrated autocorrelation time of |M| and S is at
+most 0.9 configurations in every file, so the configurations are effectively
+independent.
 2D, κ = 0.2705, λ = 0.022
+| L | ⟨φ²⟩ | ⟨S⟩/V | ⟨\|M\|⟩ | χ | U₄ | ξ₂/L |
+|---|---|---|---|---|---|---|
+| 16 | 1.5215(29) | 0.38758(49) | 0.8149(26) | 192.98(94) | 0.5524(18) | 0.7709(53) |
+| 32 | 1.4698(19) | 0.39297(26) | 0.7147(25) | 587.3(32) | 0.5672(16) | 0.7374(53) |
+| 64 | 1.4400(11) | 0.39619(18) | 0.6019(26) | 1696(11) | 0.5551(20) | 0.6512(55) |
+| 128 | 1.41936(61) | 0.398604(90) | 0.4446(23) | 4011(32) | 0.4815(27) | 0.4797(38) |
 3D, κ = 0.1923, λ = 0.9
+| L | ⟨φ²⟩ | ⟨S⟩/V | ⟨\|M\|⟩ | χ | U₄ | ξ₂/L |
+|---|---|---|---|---|---|---|
+| 16 | 0.62329(34) | −0.12466(49) | 0.2119(24) | 227.3(42) | 0.4681(65) | 0.6478(99) |
+| 32 | 0.61929(11) | −0.11846(16) | 0.1497(14) | 906(12) | 0.4721(64) | 0.6576(75) |
+| 64 | 0.617963(58) | −0.116385(81) | 0.1125(12) | 3959(68) | 0.5032(48) | 0.7127(97) |
+| 128 | 0.617684(26) | −0.116003(38) | 0.09725(87) | 22205(327) | 0.5658(35) | 0.917(12) |
+At κ = κ_c and large L, U₄ and ξ₂/L approach the Ising values 0.6107 and 0.9050 in 2D
+(Salas and Sokal, J. Stat. Phys. 98, 551 (2000)) and 0.4655 and 0.6431 in 3D
+(Hasenbusch, Phys. Rev. B 82, 174433 (2010)).