Phase transition and thermal order-by-disorder in the pyrochlore antiferromagnet Er<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mrow/><mml:mn>2</mml:mn></mml:msub></mml:math>Ti<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mrow/><mml:mn>2</mml:mn></mml:msub></mml:math>O<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mrow/><mml:mn>7</mml:mn></mml:msub></mml:math>: A high-temperature series expansion study
Bibliographic record
Abstract
We use a high-temperature series expansion method to study the phenomenon of thermal order-by-disorder in the rare-earth pyrochlore material Er${}_{2}$Ti${}_{2}$O${}_{7}$ on its approach to the critical temperature ${T}_{c}$. We show that its anisotropic exchange parameters, ${{J}_{e}}$, characterizing an effective spin-1/2 model and recently determined from high-field inelastic neutron scattering spectra, describe very well the thermodynamic properties of the material in the paramagnetic phase and near ${T}_{c}$. While different $\mathbit{q}=0$ $XY$ order-parameter susceptibilities show a high degree of degeneracy, a nonlinear susceptibility, related to the sixth power of the order parameter, reveals a thermal order-by-disorder selection of the same noncollinear ``${\ensuremath{\psi}}_{2}$ state'' as found in Er${}_{2}$Ti${}_{2}$O${}_{7}$. Our results provide a rather definite quantitative demonstration that thermal order-by-disorder is operating at ${T}_{c}$ in this frustrated quantum spin-1/2 antiferromagnetic material.
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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 | 0.000 |
| 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 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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".