Structures of group-15 elemental solids from an effective boundary theory
Bibliographic record
Abstract
We present an effective description for the crystal structures of pnictogen elemental solids. In these materials, each atom contains three valence electrons in $p$ orbitals. They are shared between neighbouring atoms to form valence bonds. We propose a trivalent network model on the simple cubic lattice. As a generalization of a dimer model, we impose a constraint that three dimers must touch every site. We argue that intra-orbital Coulomb repulsion prohibits the formation of two adjacent, parallel dimers. This leads to a tripod-like local configuration at every site. More importantly, it forces every line of the cubic lattice to have alternating dimers and blanks. There is no dynamics as dimers cannot be locally rearranged. A bulk-boundary mapping emerges whereby bonds in the interior are fully described by Ising variables on three bounding planes -- a simple example of holography that may be realized in real materials. To describe the energetics of bonding, we formulate a minimal model in terms of boundary Ising spins. Symmetries reduce the problem to that of three identical, independent, two-dimensional Ising models. An antiferromagnetic Ising-ground-state corresponds to the A7 structure seen in antimony and grey arsenic. An antiferromagnetic phase within a bilayer describes the structure of phosphorene. By stacking such bilayers, we obtain the A17 structure of black phosphorus. The stripe phase of the Ising models describes the cubic gauche structure of nitrogen. As a testable signature, we demonstrate that single impurities will induce long-ranged domain walls.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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".