Lifshitz-like black brane thermodynamics in higher dimensions
Bibliographic record
Abstract
Gravitational backgrounds in $d+2$ dimensions have been proposed as holographic duals to Lifshitz-like theories describing critical phenomena in $d+1$ dimensions with critical exponent $z\ensuremath{\ge}1$. We numerically explore a dilaton Einstein-Maxwell model, admitting such backgrounds as solutions. Such backgrounds are characterized by a temperature $T$ and chemical potential $\ensuremath{\mu}$, and we find how to embed these solutions into anti-de Sitter (AdS) for a range of values of $z$ and $d$. We find no thermal instability going from the $T\ensuremath{\ll}\ensuremath{\mu}$ to the $T\ensuremath{\gg}\ensuremath{\mu}$ regimes, regardless of the dimension, and find that the solutions smoothly interpolate between Lifshitz-like behavior and relativistic AdS-like behavior. We show, using some conserved, that the energy density $\mathcal{E}$, entropy density $s$, and number density $n$ are related via $\mathcal{E}=\frac{d}{d+1}(Ts+\ensuremath{\mu}n)$, as is required by the isometries of ${\mathrm{AdS}}_{d+2}$. Finally, in the $T\ensuremath{\ll}\ensuremath{\mu}$ regime, the entropy density is found to satisfy a power law $s\ensuremath{\propto}c{T}^{d/z}{\ensuremath{\mu}}^{(z\ensuremath{-}1)d/z}$, and we numerically explore the dependence of the constant $c$, a measure of the number of degrees of freedom, on $d$ and $z$.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".