Quantum multicriticality and emergent symmetry in Dirac systems with two order parameters at three-loop order
Bibliographic record
Abstract
Two-dimensional materials with interacting Dirac excitations can host quantum multicritical behavior near the phase boundaries of the semimetallic and two-ordered phases. We study such behavior in Gross--Neveu--Yukawa field theories where $N_f$ flavors of Dirac fermions are coupled to two order-parameter fields with $SO(N_A)$ and $SO(N_B)$ symmetry, respectively. To that end, we employ the perturbative renormalization group up to three-loop order in $4-ε$ spacetime dimensions. We distinguish two key scenarios: (i) The two orders are compatible as characterized by anticommuting mass terms, and (ii) the orders are incompatible. For the first case, we explore the stability of a quantum multicritical point with emergent $SO(N_A\!+\!N_B)$ symmetry. We find that the stability is controlled by increasing the number of Dirac fermion flavors. Moreover, we extract the series expansion of the leading critical exponents for the chiral $SO(4)$ and $SO(5)$ models up to third order in $ε$. Notably, we find a tendency towards rapidly growing expansion coefficients at higher orders, rendering an extrapolation to $ε=1$ difficult. For the second scenario, we study a model with $SO(4) \simeq SO(3) \times SO(3)$ symmetry, which was recently suggested to describe criticality of antiferromagnetism and superconductivity in Dirac systems. However, it was also argued that a physically admissible renormalization-group fixed point only exists for $N_f$ above a critical number $N_{c}^>$. We determine the corresponding series expansion at three-loop order as $N_{c}^>\approx 16.83-7.14ε-7.12ε^2$. This suggests that the physical choice of $N_f=2$ may be a borderline case, where true criticality and pseudocriticality, as induced by fixed-point annihilation, are extremely challenging to distinguish.
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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 | 0.000 |
| 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) | 0.001 | 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".