Critical Behavior of the Two-Dimensional Ising Susceptibility
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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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 | 0.000 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".