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 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".