Scaling corrections to the ground state energy of the spin-½ isotropic anti-ferromagnetic Heisenberg chain
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Bibliographic record
Abstract
Solutions to the Bethe Ansatz equations for the ground state of spin-½ isotropic anti-ferromagnetic periodic Heisenberg chains to length L = 221 are obtained by combining Lagrange interpolation with Newton–Raphson iteration. The long chain lengths allow many powers of a renormalization group running coupling constant to be included in fits to the ground state energy and make possible the confirmation of the convergence of the leading logarithmic term. The amplitude of this term is consistent with that expected on the basis of conformal field theory and the connection of the discrete spin-½ system to the continuum Wess–Zumino–Witten model. This resolves a decades old discrepancy based on analysis of shorter chains. An analytical improvement to the Hulthén wave-vector distribution is also provided.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.003 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it