Corrections to scaling in the 2D φ4 model: Monte Carlo results and some related problems
Bibliographic record
Abstract
Monte Carlo (MC) simulations have been performed to refine the estimation of the correction-to-scaling exponent ω in the 2D φ 4 model, which belongs to one of the most fundamental universality classes. If corrections have the form ∝ L −ω, then we find ω = 1.546(30) and ω = 1.509(14) as the best estimates. These are obtained from the finite-size scaling of the susceptibility data in the range of linear lattice sizes L ∈ [128, 2048] at the critical value of the Binder cumulant and from the scaling of the corresponding pseudocritical couplings within L ∈ [64, 2048]. These values agree with several other MC estimates at the assumption of the power-law corrections and are comparable with the known results of the ϵ-expansion. In addition, we have tested the consistency with the scaling corrections of the form ∝ L −4/3 , ∝ L −4/3 lnL and ∝ L −4/3/ lnL, which might be expected from some considerations of the renormalization group and Coulomb gas model. The latter option is consistent with our MC data. Our MC results served as a basis for a critical reconsideration of some earlier theoretical conjectures and scaling assumptions. In particular, we have corrected and refined our previous analysis by grouping Feynman diagrams. The renewed analysis gives ω ≈ 4 − d − 2η as some approximation for spatial dimensions d < 4, or ω ≈ 1.5 in two dimensions.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".