Tuning coupling: Discrete changes in runaway avalanche sizes in disordered media
Bibliographic record
Abstract
Hysteretic systems may exhibit a runaway avalanche in which a large fraction of the constituents of the system collectively change state. It would be very valuable to understand the role that interaction strength between constituents plays in the size of such catastrophic runaway avalanches. We use a simple model, the random field Ising model, to study how the size of the runaway avalanche changes as the coupling between spins, $J$, is tuned. In particular, we calculate $P(S)$, the distribution of size changes $S$ in the runaway avalanche size as $J$ comes close to a critical value ${J}_{c}$, and find that the distribution scales as $P(S)\ensuremath{\sim}{S}^{\ensuremath{-}\ensuremath{\tau}}\mathcal{D}({S}^{\ensuremath{\sigma}}(J/{J}_{c}\ensuremath{-}1))$, with $\ensuremath{\tau}$ and $\ensuremath{\sigma}$ critical exponents and $\mathcal{D}(x)$ a universal scaling function. In mean field theory we find $\ensuremath{\tau}=3/2$, $\ensuremath{\sigma}=1/2$, and $\mathcal{D}(x)=\mathrm{exp}[\ensuremath{-}{(3x)}^{1/\ensuremath{\sigma}}/2]$. On the basis of these results and previous studies, we also predict that for three dimensions $\ensuremath{\tau}=1.6$ and $\ensuremath{\sigma}=0.24$.
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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 | 0.000 | 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 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".