Goldstone mode singularities in O(n) models
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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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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 it