Effective Hamiltonians and dilution effects in Kagome and related anti-ferromagnets
Bibliographic record
Abstract
What is the zero-temperature ordering pattern of a Heisenberg anti-ferromagnet with large spin length S (and possibly small dilution), on the Kagome lattice, or others built from corner-sharing triangles and tetrahedra? First, I summarize the uses of effective Hamiltonians to resolve the large ground-state degeneracy, leading to long-range order of the usual kind. Secondly, I discuss the effects of dilution, in particular that the classical ground states become nonfrustrated, in that every simplex of spins is optimally satisfied. Of three explanations for this, the most satisfactory is the MoessnerChalker constraint enumeration. Quantum zero-point energy may compete with classical exchange energy in a diluted system, creating frustration and enabling a spin-glass state. I suggest that the regime of over 97% occupation is qualitatively different from the more strongly diluted regime. PACS Nos.: 75.10N, 75.50Ee, 75.40, 75.25+z
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.004 | 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".