Bootstrapping the long-range Ising model in three dimensions
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Abstract The 3D Ising model and the generalized free scalar of dimension at least 0.75 belong to a continuous line of nonlocal fixed points, each referred to as a long-range Ising model. They can be distinguished by the dimension of the lightest spin-2 operator, which interpolates between 3 and 3.5 if we focus on the non-trivial part of the fixed line. A property common to all such theories is the presence of three relevant conformal primaries, two of which form a shadow pair. This pair is analogous to a superconformal multiplet in that it enforces relations between certain conformal blocks. By demanding that crossing symmetry and unitarity hold for a set of correlators involving the relevant operators, we compute numerical bounds on their scaling dimensions and OPE coefficients. Specifically, we raise the minimal spin-2 operator dimension to find successively smaller regions which eventually form a kink. Whenever a kink appears, its co-ordinates show good agreement with the epsilon expansion predictions for the critical exponents in the corresponding statistical model. As a byproduct, our results reveal an infinite tower of protected operators with odd spin.
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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 | 0.001 | 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 it