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 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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.003 |
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".