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 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 | 0.005 | 0.003 |
| Meta-epidemiology (narrow) | 0.004 | 0.006 |
| Meta-epidemiology (broad) | 0.002 | 0.006 |
| Bibliometrics | 0.001 | 0.004 |
| Science and technology studies | 0.006 | 0.007 |
| Scholarly communication | 0.004 | 0.007 |
| Open science | 0.007 | 0.007 |
| Research integrity | 0.005 | 0.007 |
| Insufficient payload (model declined to judge) | 0.074 | 0.004 |
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; both teacher heads agree on what is shown here.
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".