Phase structure of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>C</mml:mi><mml:mi>P</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> model in the presence of a topological <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>θ</mml:mi></mml:math>-term
Bibliographic record
Abstract
We numerically study the phase structure of the $CP(1)$ model in the presence of a topological $\ensuremath{\theta}$-term, a regime afflicted by the sign problem for conventional lattice Monte Carlo simulations. Using a bond-weighted tensor renormalization group method, we compute the free energy for inverse couplings ranging from $0\ensuremath{\le}\ensuremath{\beta}\ensuremath{\le}1.1$ and find a $CP$-violating, first-order phase transition at $\ensuremath{\theta}=\ensuremath{\pi}$. In contrast to previous findings, our numerical results provide no evidence for a critical coupling ${\ensuremath{\beta}}_{c}<1.1$ above which a second-order phase transition emerges at $\ensuremath{\theta}=\ensuremath{\pi}$ and/or the first-order transition line bifurcates at $\ensuremath{\theta}\ensuremath{\ne}\ensuremath{\pi}$. If such a critical coupling exists, as suggested by Haldane's conjecture, our study indicates that is larger than ${\ensuremath{\beta}}_{c}>1.1$.
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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 | 0.003 | 0.002 |
| Meta-epidemiology (narrow) | 0.002 | 0.003 |
| Meta-epidemiology (broad) | 0.002 | 0.005 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.005 | 0.005 |
| Research integrity | 0.001 | 0.005 |
| Insufficient payload (model declined to judge) | 0.001 | 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; both teacher heads agree on what is shown here.
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".