Addendum-erratum to: “Nonasymptotic critical behavior from field theory at d = 3. II. The ordered-phase case”
Bibliographic record
Abstract
This note is intended to emphasize the existence of estimated Feynman integrals in three dimensions for the free energy of the O(1) scalar theory up to five loops which may be useful for other work. We also correct some misprints of the published paper. We present the corrected table I of the original paper [1] which displays the values of the Feynman integrals of the O(1) scalar theory contributing to the free energy up to five loops and their symmetry factors. The values differ from those Feynman integrals previously calculated in [2] 1 due to the necessity of introducing a “soft ” mass parameter instead of the usual renormalized (at zero-momentum) mass (see the text of the original paper [1] and [3] for details). Consequently, many of the estimates of Feynman Integrals presented in table I have been extracted from [2] by accounting for a harmless 3-d renormalization in order to get a soft-mass parameter (characterizing a minimal subtraction scheme similar to that introduced in [4]). Since the five-loop contributions to the free energy involves ϕ 3 vertices mixed to ϕ 4 vertices, Feynman integrals which are different or cannot be obtained from those previously considered in [2] have been estimated in three dimensions for the occasion 2. These are: • the four-loop integrals with Heap’s numbers 13–17 (column h in the following table I, see table IV of [5]). They involve only ϕ 3 vertices. They have been estimated and successfully compared to similar calculations extracted from [6]. • the five-loop integrals with Heap’s numbers 80–102 (see table V of [5]). They involve ϕ 3 vertices mixed with a single ϕ 4 vertex. They have been calculated exclusively for this work. • the five-loop integrals with Heap’s numbers 103–118 (see table V of [5]). They involve only ϕ 3 vertices. They have been calculated for this work and successfully compared to similar calculations extracted from [7]. 1 The unpublished Guelph report [2] may be obtained via H. Kleinert and V. Schulte-Frohlinde web site at
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.010 |
| Meta-epidemiology (narrow) | 0.002 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.003 | 0.001 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.075 | 0.028 |
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 source (direct Gemma or distilled Codex), 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".