Stability of icosahedral quasicrystals in a simple model with two-length scales
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Bibliographic record
Abstract
The phase behaviour of a free energy functional with two length scales is examined by comparing the free energy of different candidate phases including three-dimensional icosahedral quasicrystals. Accurate free energy of the quasicrystals has been obtained using the recently developed projection method. The results reveal that the icosahedral quasicrystal and body-centred-cubic spherical phase are the stable ordered phases of the model. Furthermore, the difference between the results obtained from the projection method and the one-mode approximation has been analyzed in detail. The present study extends previous results on two-dimensional systems, demonstrating that the interactions between density waves at two length scales can stabilize two- and three-dimensional quasicrystals.
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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 | 0.001 |
| 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 it