Bibliographic record
Abstract
Monte Carlo (MC) analysis of the Goldstone mode singularities for the transverse and the longitudinal correlation functions, behaving as G (k) ak - and G (k) bk - in the ordered phase at k 0, is performed in the three-dimensional O(n) models with n = 2,4,10. Our aim is to test some challenging theoretical predictions, according to which the exponents and are non-trivial (3/2 < < 2 and 0 < < 1 in three dimensions) and the ratio bM 2 /a 2 (where M is a spontaneous magnetization) is universal. The trivial standardtheoretical values are = 2 and = 1. Our earlier MC analysis gives = 1.955 0.020 and about 0.9 for the O(4) model. A recent MC estimation of , assuming corrections to scaling of the standard theory, yields = 0.690.10 for the O(2) model. Currently, we have performed a similar MC estimation for the O(10) model, yielding = 1.9723(90). We have observed that the plot of the effective transverse exponent for the O(4) model is systematically shifted down with respect to the same plot for the O(10) model by = 0.0121(52). It is consistent with the idea that 2 - decreases for large n and tends to zero at n . We have also verified and confirmed the expected universality of bM 2 /a 2 for the O(4) model, where simulations at two different temperatures (couplings) have been performed.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".