Large-coordination-number expansion of a lattice Bose gas at finite temperature
Bibliographic record
Abstract
The expansion of the partition function for large coordination number $Z$ is a long-standing method and has formerly been used to describe the Ising model at finite temperatures. We extend this approach and study the interacting Bose gas at finite temperatures. An analytical expression for the free energy is derived which is valid for weakly interacting and strongly interacting bosons. The transition line which separates the superfluid phase from Mott insulating or normal gas phase is shown for fillings $\ensuremath{\langle}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{n}\ensuremath{\rangle}=1$ and $\ensuremath{\langle}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{n}\ensuremath{\rangle}=2$. For unit filling, our findings agree qualitatively with quantum Monte Carlo results. Contrary to the well-known mean-field result, the shift of the critical temperature in the weakly interacting regime is apparent.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".