Beyond one-loop calculation: Higher-order effects on Gross-Neveu-Yukawa tensorial criticality
Bibliographic record
Abstract
We study the Gross-Neveu-Yukawa field theory for the $\mathrm{SO}(N$) symmetric traceless rank-2 tensor order parameter coupled to Majorana fermions using the $\ensuremath{\epsilon}$-expansion around upper critical dimensions of $3+1$ to two loops. Previously we established in the one-loop calculation that the theory does not exhibit a critical fixed point for $N\ensuremath{\ge}4$, but that nevertheless the stable fixed point inevitably emerges at a large number ${N}_{f}$ of fermion flavors. For ${N}_{f}<{N}_{f,c1}\ensuremath{\approx}N/2$, no critical fixed point exists; for ${N}_{f,c1}<{N}_{f}<{N}_{f,c2}$, a real critical fixed point emerges from the complex plane but fails to satisfy the additional stability conditions necessary for a continuous phase transition; and finally only for ${N}_{f}>{N}_{f,c2}\ensuremath{\approx}N$ does the fixed point satisfy the stability conditions as well. In the present work we compute the $O(\ensuremath{\epsilon})$ (two-loop) corrections to the critical flavor numbers ${N}_{f,c1}$ and ${N}_{f,c2}$. Most importantly, we observe a sharp decrease in ${N}_{f,c2}$ from its one-loop value, which brings it closer to the point ${N}_{f}=1$ relevant to the standard Gross-Neveu model. Some three-loop results are also presented and discussed.
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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 | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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".