Effects of different 3D QED vertex <i>Ansätze</i> on the critical coupling
Bibliographic record
Abstract
We study the semimetal-insulator phase transition in graphene using a Schwinger-Dyson approach. We consider various forms of vertex Ans\"atze to truncate the hierarchy of Schwinger-Dyson equations. We define a Ball-Chiu-type vertex that truncates the equations without violating gauge invariance. We show that there is a family of these vertices, parametrized by a continuous parameter that we call $a$, all of which satisfy the Ward identity. We have calculated the critical coupling of the phase transition using different values of $a$. We have also tested a common approximation in which only the first term in the Ball-Chiu Ansatz is included. This vertex is independent of $a$, and, although it is not gauge invariant, it has been used many times in the literature because of the numerical simplifications it provides. We have found that, with a one-loop photon polarization tensor, the results obtained for the critical coupling from the truncated vertex and the full vertex with $a=1$ agree very well, but other values of $a$ give significantly different results. We have also done a fully self-consistent calculation, in which the photons are backcoupled to the fermion degrees of freedom, for one choice $a=1$. Our results show that when photon dynamics are correctly taken into account, it is no longer true that the truncated vertex and the full Ball-Chiu vertex with $a=1$ agree well. The conclusion is that traditional vertex truncations do not really make sense in a system that does not respect Lorentz invariance, like graphene, and the need to include vertex contributions self-consistently is likely inescapable.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| 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".