Fisher zeros of a unitary Bose gas
Bibliographic record
Abstract
For real inverse temperature β, the canonical partition function is always positive, being a sum of positive terms. There are zeros, however, on the complex β plane that are called Fisher zeros. In the thermodynamic limit, the Fisher zeros coalesce into continuous curves. In case there is a phase transition, the zeros tend to pinch the real-β axis. For an ideal trapped Bose gas in an isotropic three-dimensional harmonic oscillator, this tendency is clearly seen, signalling Bose–Einstein condensation (BEC). The calculation can be formulated exactly in terms of the virial expansion with temperature-dependent virial coefficients. When the second virial coefficient of a strongly interacting attractive unitary gas is included in the calculation, BEC seems to survive, with the condensation temperature shifted to a lower value for the unitary gas. This shift is consistent with a direct calculation of the heat capacity from the canonical partition function of the ideal and the unitary gas.
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How this classification was reachedexpand
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".