Ice on curved surfaces: Defect rings and differential local dynamics
Bibliographic record
Abstract
Ice systems are prototypes of locally constrained dynamics. This is exemplified in Coulomb-liquid phases where a large space of configurations is sampled, each satisfying local ice rules. Dynamics proceeds through ``flipping'' rings, i.e., through reversing arrows running along the edges of a polygon. We examine the role of defect rings in such phases, with square ice as a testing ground. When placed on a curved surface, the underlying square lattice will form defects such as triangles or pentagons. We show that triangular defects are statistically more ``flippable'' than the background. In contrast, pentagons and larger polygons are less flippable. In fact, flippability decreases monotonically with ring size, as seen from a Pauling-like argument. As an explicit demonstration, we wrap the square-ice model on a sphere. We start from an octahedron and perform repeated rectifications, producing a series of clusters with sphere-like geometry. They contain a fixed number of defect triangles in an otherwise square lattice. We numerically enumerate all ice-rule-satisfying configurations. Indeed, triangles are flippable in a larger fraction of configurations than quadrilaterals. The obtained flippabilities are in broad agreement with our Pauling-like estimates. We construct two minimal models for dynamics: (i) a classical model with stochastic dynamics and (ii) a quantum model with tunneling terms that flip rings. The steady state in the former (and the ground state in the latter) has contributions from all ice configurations. The dominant contribution to dynamics (or kinetic energy) comes from localized resonance within triangles. Our results suggest local dynamics as a promising observable for experiments in spin-ice and artificial-ice systems. They also point to hierarchical dynamics in materials such as ice V that contain rings of multiple sizes.
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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) | 0.001 | 0.001 |
| 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 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.001 |
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".