Abelian Higgs model at four loops, fixed-point collision, and deconfined criticality
Bibliographic record
Abstract
The Abelian Higgs model is the textbook example for the superconducting transition and the Anderson-Higgs mechanism, and has become pivotal in the description of deconfined quantum criticality. We study the Abelian Higgs model with $n$ complex scalar fields at unprecedented four-loop order in the $4\ensuremath{-}\ensuremath{\epsilon}$ expansion and find that the annihilation of the critical and bicritical points occurs at a critical number of ${n}_{c}\ensuremath{\approx}182.95\left(1\ensuremath{-}1.752\ensuremath{\epsilon}+0.798{\ensuremath{\epsilon}}^{2}+0.362{\ensuremath{\epsilon}}^{3}\right)+O\left({\ensuremath{\epsilon}}^{4}\right)$. Consequently, below ${n}_{c}$, the transition turns from second to first order. Resummation of the series to extract the result in three dimensions provides strong evidence for a critical ${n}_{c}(d=3)$ which is significantly below the leading-order value, but the estimates for ${n}_{c}$ are widely spread. Conjecturing the topology of the renormalization group flow between two and four dimensions, we obtain a smooth interpolation function for ${n}_{c}(d)$ and find ${n}_{c}(3)\ensuremath{\approx}12.2\ifmmode\pm\else\textpm\fi{}3.9$ as our best estimate in three dimensions. Finally, we discuss Miransky scaling occurring below ${n}_{c}$ and comment on implications for weakly first-order behavior of deconfined quantum transitions. We predict an emergent hierarchy of length scales between deconfined quantum transitions corresponding to different $n$.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".