Shattering in the Ising p-spin glass model
Bibliographic record
Abstract
Abstract We study the Ising p -spin glass model for large p . We show that for any inverse temperature $$\sqrt{\ln 2}<\beta <\sqrt{2\ln 2}$$ ln 2 < β < 2 ln 2 and any large p , the model exhibits shattering : w.h.p. as $$n\rightarrow \infty $$ n → ∞ , there exists exponentially many well-separated clusters such that (a) each cluster has exponentially small Gibbs mass, and (b) the clusters collectively contain all but a vanishing fraction of Gibbs mass. Moreover, these clusters consist of configurations with energy near $$\beta $$ β . Range of temperatures for which shattering occurs is within the replica symmetric region. To the best of our knowledge, this is the first shattering result regarding the Ising p -spin glass models. Furthermore, we show that for any $$\gamma >0$$ γ > 0 and any large enough p , the model exhibits an intricate geometrical property known as the multi Overlap Gap Property above the energy value $$\gamma \sqrt{2\ln 2}$$ γ 2 ln 2 . Our proofs are elementary, and in particular based on simple applications of the first and the second moment methods.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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 source (direct Gemma or distilled Codex), 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".