Magic number behavior for heat capacities of medium sized classical Lennard-Jones clusters
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Bibliographic record
Abstract
Monte Carlo methods were used to calculate heat capacities as functions of temperature for classical atomic clusters of aggregate sizes $25 \\leq N \\leq 60$ that were bound by pairwise Lennard-Jones potentials. The parallel tempering method was used to overcome convergence difficulties due to quasiergodicity in the solid-liquid phase-change regions. All of the clusters studied had pronounced peaks in their heat capacity curves, most of which corresponded to their solid-liquid phase-change regions. The heat capacity peak height and location exhibited two general trends as functions of cluster size: for $N = 25$ to 36, the peak temperature slowly increased, while the peak height slowly decreased, disappearing by $N = 37$; for $N = 30$, a very small secondary peak at very low temperature emerged and quickly increased in size and temperature as $N$ increased, becoming the dominant peak by $N = 36$. Superimposed on these general trends were smaller fluctuations in the peak heights that corresponded to ``magic number'' behavior, with local maxima found at $N = 36, 39, 43, 46$ and 49, and the largest peak found at $N = 55$. These magic numbers were a subset of the magic numbers found for other cluster properties, and can be largely understood in terms of the clusters' underlying geometries. Further insights into the melting behavior of these clusters were obtained from quench studies and by examining rms bond length fluctuations.
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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 | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.026 | 0.003 |
Machine scores (provisional)
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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