The absence of phase transition for the classical XY-model on Sierpinski\n pyramid with fractal dimension D=2
Bibliographic record
Abstract
For the spin models with continuous symmetry on regular lattices and finite\nrange of interactions the lower critical dimension is d=2. In two dimensions\nthe classical XY-model displays Berezinskii-Kosterlitz-Thouless transition\nassociated with unbinding of topological defects (vortices and antivortices).\nWe perform a Monte Carlo study of the classical XY-model on Sierpinski pyramids\nwhose fractal dimension is D=log4/log2=2 and the average coordination number\nper site is about 7. The specific heat does not depend on the system size which\nindicates the absence of long range order. From the dependence of the helicity\nmodulus on the cluster size and on boundary conditions we draw a conclusion\nthat in the thermodynamic limit there is no Berezinskii-Kosterlitz-Thouless\ntransition at any finite temperature. This conclusion is also supported by our\nresults for linear magnetic susceptibility. The lack of finite temperature\nphase transition is presumably caused by the finite order of ramification of\nSierpinski pyramid.\n
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| 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 | 0.000 |
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".