A first course in the Yang–Baxter equation
Bibliographic record
Abstract
A crash course on the Yang–Baxter equation and its applications in the statistical mechanics of lattice vertex models is presented. Using the simple example of a one-dimensional lattice gas, the basic terminology and standard mathematical procedures of statistical mechanics are illustrated. The coproduct notation is introduced via a discussion of the two-dimensional dimer model, and the transfer matrix formulation is elaborated further. The algebraic Bethe Ansatz (ABA) is introduced in the context of the ice model, leading to the Yang–Baxter equations. The motivation for introducing the ABA is developed, emphasizing the similarity to the quantum oscillator problem, in features such as the generation of “excited states”, and the determination of the eigenvalue spectrum. Finally, these methods from the theory of lattice models are applied to the case of a quantum many-body problem, the Heisenberg chain. From the condition that the monodromy matrices satisfy the Yang–Baxter equation, a complete set of mutually commuting operators is derived, and the Heisenberg chain problem is completely solved.PACS Nos.: 02.20.Uw, 24.10.Cn, 87.10.Hk, 05.20.–y
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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 | 0.000 | 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 | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| 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 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".