Critical behavior of the compactified λϕ4 theory
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Bibliographic record
Abstract
We investigate the critical behavior of the N-component Euclidean λϕ4 model, in the large N limit, in three situations: confined between two parallel planes a distance L apart from one another; confined to an infinitely long cylinder having a square transversal section of area L2; and to a cubic box of volume L3. Taking the mass term in the form m02=α(T−T0), we retrieve Ginzburg–Landau models which are supposed to describe samples of a material undergoing a phase transition, respectively, in the form of a film, a wire and of a grain, whose bulk transition temperature (T0) is known. We obtain equations for the critical temperature as functions of L and of T0, and determine the limiting sizes sustaining the transition.
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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