Phase diagrams of site-frustrated Heisenberg models on simple cubic, bcc, and fcc lattices
Bibliographic record
Abstract
We have determined the phase diagrams of the site-frustrated Heisenberg model in three dimensions over the entire concentration regime of competing ferromagnetic (F) and antiferromagnetic (A) sites for the three basic lattice types: simple cubic (sc), body-centered cubic (bcc) and face-centered cubic (fcc) using Monte Carlo methods. Long-range ferromagnetic (FM) or antiferromagnetic (AF) order is established at a finite temperature, second-order phase transition whenever F or A sites percolate. Since site percolation thresholds in three dimensions are less than $\frac{1}{2}$, FM and AF order coexist over a wide composition regime. The only apparent effect of frustration is to cause the AF and FM order to occur perpendicular to one another. Strong evidence is found to suggest that all of the transitions remain in the Heisenberg universality class and that there exists a tetracritical point at $x=\frac{1}{2}$ where ${T}_{C}={T}_{N}$.
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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) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".