Bootstrapping frustrated magnets: the fate of the chiral ${\rm O}(N)\times {\rm O}(2)$ universality class
Bibliographic record
Abstract
We study multiscalar theories with \text{O}(N) × \text{O}(2) O ( N ) × O ( 2 ) symmetry. These models have a stable fixed point in d d dimensions if N N is greater than some critical value N_c(d) N c ( d ) . Previous estimates of this critical value from perturbative and non-perturbative renormalization group methods have produced mutually incompatible results. We use numerical conformal bootstrap methods to constrain N_c(d) N c ( d ) for 3 ≤ d < 4 3 ≤ d < 4 . Our results show that N_c> 3.78 N c > 3.78 for d = 3 d = 3 . This favors the scenario that the physically relevant models with N = 2,3 N = 2 , 3 in d=3 d = 3 do not have a stable fixed point, indicating a first-order transition. Our result exemplifies how conformal windows can be rigorously constrained with modern numerical bootstrap algorithms.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.003 | 0.003 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.008 | 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".