Explosive Percolation is Continuous, but with Unusual Finite Size Behavior
Why this work is in the frame
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Bibliographic record
Abstract
We study four Achlioptas-type processes with ``explosive'' percolation transitions. All transitions are clearly continuous, but their finite size scaling functions are not entirely holomorphic. The distributions of the order parameter, i.e., the relative size ${s}_{\mathrm{max}}/N$ of the largest cluster, are double humped. But---in contrast to first-order phase transitions---the distance between the two peaks decreases with system size $N$ as ${N}^{\ensuremath{-}\ensuremath{\eta}}$ with $\ensuremath{\eta}>0$. We find different positive values of $\ensuremath{\beta}$ (defined via $⟨{s}_{\mathrm{max}}/N⟩\ensuremath{\sim}(p\ensuremath{-}{p}_{c}{)}^{\ensuremath{\beta}}$ for infinite systems) for each model, showing that they are all in different universality classes. In contrast, the exponent $\ensuremath{\Theta}$ (defined such that observables are homogeneous functions of $(p\ensuremath{-}{p}_{c}){N}^{\ensuremath{\Theta}}$) is close to---or even equal to---$1/2$ for all models.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| 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