Scale-invariant magnetic anisotropy in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>α</mml:mi> <mml:mtext>−</mml:mtext> <mml:msub> <mml:mi>RuCl</mml:mi> <mml:mn>3</mml:mn> </mml:msub> </mml:mrow> </mml:math> : A quantum Monte Carlo study
Bibliographic record
Abstract
We compute the rotational anisotropy of the free energy of $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$ in an external magnetic field. This quantity, known as the magnetotropic susceptibility, $k$, relates to the second derivative of the free energy with respect to the angle of rotation. We have used approximation-free, auxiliary-field quantum Monte Carlo simulations for a realistic model of $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$ and optimized the path integral to alleviate the negative sign problem. This allows us to reach temperatures down to $30\phantom{\rule{0.16em}{0ex}}\mathrm{K}$---an energy scale below the dominant Kitaev coupling. We demonstrate that the magnetotropic spin susceptibility in this model of $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$ displays scaling behavior $k=Tf(B/T)$ at high temperatures. Once the uniform susceptibility departs from the Curie law (i.e., at the energy scale of the exchange interactions), it appears to transition to an emergent scalinglike behavior, characterized by a different function $f$ at lower temperatures, stemming from the locality of torque fluctuations. We observe a remarkable numerical match between experiment and simulations and we also find qualitative agreement with the pure Kitaev model. In comparison, for the XXZ Heisenberg Hamiltonian, the scaling $k=Tf(B/T)$ breaks down at a temperature scale where the uniform spin susceptibility deviates from the Curie law and never reemerges at low temperatures.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.017 | 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".