Quantum Critical Points with the Coulomb Interaction and the Dynamical Exponent: When and Why<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">z</mml:mi><mml:mspace/><mml:mo>=</mml:mo><mml:mspace/><mml:mn>1</mml:mn><mml:mn/></mml:math>
Bibliographic record
Abstract
A general scenario that leads to Coulomb quantum criticality with the dynamical critical exponent $z\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ is proposed. I point out that the long-range Coulomb interaction and quenched disorder have competing effects on $z$, and that balance between the two may lead to charged quantum critical points at which $z\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ exactly. This is illustrated with the calculation for the Josephson junction array Hamiltonian in dimensions $D\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3\ensuremath{-}\ensuremath{\epsilon}$. Precisely in $D\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3$, however, the above simple result breaks down, and $z>1$. Relation to other studies is discussed.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".