fcc antiferromagnetic Ising model in a uniform external field solved by mean-field theory
Bibliographic record
Abstract
The fcc antiferromagnetic Ising model with nearest-neighbor interactions in a uniform external field is studied using a simple mean-field theory, and a phase diagram is presented. Our theory is formulated in the spirit of a Weiss-like molecular field theory: Four spins forming a basic tetrahedron are allowed to fluctuate while the surrounding 28 spins take mean-field values. The phase diagram is similar to that obtained in the Bragg-Williams approximation for chemical ordering of ${\mathrm{Cu}}_{1\ensuremath{-}x}{\mathrm{Au}}_{x}$ alloys, although apart from the similar phase diagrams, the two theories give substantially different results. First, all of the detected transitions are correctly predicted to be first order. Second, we obtain two previously undetected reentrant phases. The existence of reentrant phases is discussed and we show that this ordering scenario is fully consistent with the results of the Bragg-Williams approximation which does not contain reentrant phases.
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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) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".