Designing a minimal Landau model to stabilize desired quasicrystals
Bibliographic record
Abstract
Interparticle interactions with multiple length scales play a pivotal role in the formation and stability of quasicrystals. Choosing a minimal set of length scales to stabilize a given quasicrystal is a challenging problem. To address this challenge, we propose a symmetry-preserving screening method (SPSM) to design a Landau theory with a minimal number of length scales—referred to as the minimal Landau theory—that includes only the essential length scales necessary to stabilize quasicrystals. Based on a generalized multiple-length-scale Landau theory, SPSM first evaluates various spectral configurations of candidate structures under a hard constraint. It then identifies the configuration with the lowest free energy. Using this optimal configuration, SPSM calculates phase diagrams to explore the thermodynamic stability of desired quasicrystals. SPSM can design a minimal Landau theory capable of stabilizing the desired quasicrystals by incrementally increasing the number of length scales. Our application of SPSM has not only confirmed known behaviors in 10- and 12-fold quasicrystals but also led to a significant prediction that quasicrystals with 8-, 14-, 16-, and 18-fold symmetry could be stable within three-length-scale Landau models.
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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 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 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".