Advanced Monte Carlo Study of the Goldstone Mode Singularity in the 3D XY Model
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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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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 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.003 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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