Corrections to scaling in the 3D Ising model: A comparison between MC and MCRG results
Bibliographic record
Abstract
Corrections to scaling in the 3D Ising model are studied based on Monte Carlo (MC) simulation results for very large lattices with linear lattice sizes up to [Formula: see text]. Our estimated values of the correction-to-scaling exponent [Formula: see text] tend to decrease below the usually accepted value about 0.83 when the smallest lattice sizes, i.e. [Formula: see text] with [Formula: see text], are discarded from the fits. This behavior apparently confirms some of the known estimates of the Monte Carlo renormalization group (MCRG) method, i.e. [Formula: see text] and [Formula: see text]. We discuss the possibilities that [Formula: see text] is either really smaller than usually expected or these values of [Formula: see text] describe some transient behavior which, eventually, turns into the correct asymptotic behavior at [Formula: see text]. We propose refining MCRG simulations and analysis to resolve this issue. Our actual MC estimations of the critical exponents [Formula: see text] and [Formula: see text] provide stable values [Formula: see text] and [Formula: see text], which well agree with those of the conformal bootstrap method, i.e. [Formula: see text] and [Formula: see text].
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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 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 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".