Critical Behavior of the Two-Dimensional Ising Susceptibility
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Bibliographic record
Abstract
We report computations of the short- and long-distance (scaling) contributions to the square-lattice Ising susceptibility. Both computations rely on summation of correlation functions, obtained using nonlinear partial difference equations. In terms of a temperature variable $\ensuremath{\tau}$, linear in ${T/T}_{c}\ensuremath{-}1$, the short-distance terms have the form ${\ensuremath{\tau}}^{p}(\mathrm{ln}|\ensuremath{\tau}|{)}^{q}$ with $p\ensuremath{\ge}{q}^{2}$. A high- and low-temperature series of $N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}323$ terms, generated using an algorithm of complexity $\mathrm{O}({N}^{6})$, are analyzed to obtain the scaling part, which when divided by the leading $|\ensuremath{\tau}{|}^{\ensuremath{-}7/4}$ singularity contains only integer powers of $\ensuremath{\tau}$. Contributions of distinct irrelevant variables are identified and quantified at leading orders $|\ensuremath{\tau}{|}^{9/4}$ and $|\ensuremath{\tau}{|}^{17/4}$.
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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 | 0.000 |
| 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