Quantum critical scaling in magnetic field near the Dirac point in graphene
Bibliographic record
Abstract
Motivated by the recent measurement of the activation energy at the quantum Hall state at the filling factor $f=1$ in graphene, we discuss the scaling of the interaction-induced gaps in the vicinity of the Dirac point with the magnetic field. The gap at $f=1$ is shown to be bounded from above by $E(1)/C$, where $E(n)={v}_{F}\sqrt{2nB}$ is the Landau-level energy and $C=5.985+O(1/N)$ is a universal number. The universal scaling functions are computed exactly for a large number of Dirac fermions $N$. We find a sublinear dependence of the gap at the laboratory fields of $10\text{ }\text{T}<B<50\text{ }\text{T}$ for realistic values of short-range repulsion between electrons, in quantitative agreement with observation.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".