Fractalization drives crystalline states in a frustrated spin system
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Bibliographic record
Abstract
The fractalized Hofstadter butterfly energy spectrum predicted for magnetically confined fermions diffracted by a crystal lattice has remained beyond the reach of laboratory-accessible magnetic fields. We find the geometrically frustrated spin system SrCu(2)(BO(3))(2) to provide a sterling demonstration of a system in which bosons confined by a magnetic and lattice potential mimic the behavior of fermions in the extreme quantum limit, giving rise to a sequence of plateaus at all magnetization m(z)/m(sat) = 1/q ratios 9 > or = q > or = 2 and p/q = 2/9 (m(sat) is the saturation magnetization) in magnetic fields up to 85 T and temperatures down to 29 mK, within the sequence of previously identified plateaus at 1/8, 1/4, and 1/3 of the saturated magnetization. We identify this hierarchy of plateaus as a consequence of confined bosons in SrCu(2)(BO(3))(2) mimicking the high magnetic field fractalization predicted by the Hofstadter butterfly for fermionic systems. Such an experimental realization of the Hofstadter problem for interacting fermions has not been previously achieved in real materials, given the unachievably high magnetic flux densities or large lattice periods required. By a theoretical treatment that includes short-range repulsion in the Hofstadter treatment, stripe-like spin density-modulated phases are revealed in SrCu(2)(BO(3))(2) as emergent from a fluidic fractal spectrum.
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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 | 0.001 |
| 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 it