Advanced Monte Carlo Study of the Goldstone Mode Singularity in the 3D XY Model
Bibliographic record
Abstract
Advanced Monte Carlo simulations of magnetisation and susceptibility in 3D XY model are performed at two different coupling constants β =0.55 and β =0.5, completing our previous simulation results with additional data points and extending the range of the external field to twice as small values as previously reported (h ≥ 0.00015625). The simulated maximal lattices sizes are also increased from L=384 to L=512. Our aim is an improved estimation of the exponent ρ, describing the Goldstone mode singularity M(h) = M(+0)+chρ at h → 0, where M is the magnetisation. The data reveal some unexpected small oscillations. It makes the estimation by many-parameter fits of the magnetisation data unstable, and we are looking for an alternative method. Our best estimate ρ = 0.555(17) is extracted from the analysis of effective exponents determined from local fits of the susceptibility data. This method gives stable and consistent results for both values of β, taking into account the leading as well as the subleading correction to scaling. We report also the values of spontaneous magnetisation.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 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".