Large-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi></mml:math>estimates of universal amplitudes of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="double-struck">C</mml:mi><mml:msup><mml:mi mathvariant="double-struck">P</mml:mi><mml:mrow><mml:mi>N</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>theory and comparison with a<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mstyle scriptlevel="1"><mml:mfrac bevelled="false"><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:mstyle></mml:mrow></mml:math>square-lattice model with competing four-spin interactions
Bibliographic record
Abstract
We present computations of certain finite-size scaling functions and universal amplitude ratios in the large-$N$ limit of the $\mathbb{C}{\mathbb{P}}^{N\ensuremath{-}1}$ field theory. We pay particular attention to the uniform susceptibility, the spin stiffness, and the specific heat. Field theoretic arguments have shown that the long-wavelength description of the phase transition between the N\'eel and valence-bond solid states in square lattice $S=1/2$ antiferromagnets is expected to be the noncompact $\mathbb{C}{\mathbb{P}}^{1}$ field theory. We provide a detailed comparison between our field theoretic calculations and quantum Monte Carlo data close to the N\'eel-VBS transition on a $S=1/2$ square-lattice model with competing four-spin interactions (the JQ model).
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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 | 0.002 | 0.005 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.005 | 0.003 |
| Science and technology studies | 0.002 | 0.001 |
| Scholarly communication | 0.004 | 0.007 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.187 | 0.058 |
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".