Derivation of the low-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>T</mml:mi></mml:math>phase diagram of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mtext>LiHo</mml:mtext></mml:mrow><mml:mi>x</mml:mi></mml:msub><mml:msub><mml:mtext>Y</mml:mtext><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mtext>F</mml:mtext><mml:mn>4</mml:mn></mml:msub></mml:mrow></mml:math>: A dipolar quantum Ising magnet
Bibliographic record
Abstract
The ${\text{LiHo}}_{x}{\text{Y}}_{1\ensuremath{-}x}{\text{F}}_{4}$ compound is widely considered to be the archetypal dipolar quantum Ising system, with longitudinal dipolar interactions ${V}_{ij}^{zz}$ between Ho spins ${i,j}$ competing with transverse field--induced tunneling, to give a $T=0$ quantum phase transition. By varying the Ho concentration $x$, the typical strength ${V}_{0}$ of ${V}_{ij}^{zz}$ can be varied over many orders of magnitude, and so can the transverse field ${H}_{\ensuremath{\perp}}$. A new effective Hamiltonian is derived, starting from the electronuclear degrees of freedom, which is valid at low and intermediate temperatures. For any such dipolar quantum Ising system, the hyperfine interaction will dominate the physics at low temperatures, even if its strength ${A}_{0}<{V}_{0}$: One must therefore go beyond an electronic transverse field quantum Ising model. We derive the full phase diagram of this system, including all nuclear levels, as a function of transverse field ${H}_{\ensuremath{\perp}}$, temperature $T$, and dipole concentration $x$. For ${\text{LiHo}}_{x}{\text{Y}}_{1\ensuremath{-}x}{\text{F}}_{4}$ we predict a re-entrant critical field as a function of $x$. We also predict the phase diagram for $x=0.045$ and the behavior of the system in magnetic-resonance and muon-spin-relaxation experiments.
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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 | 0.006 | 0.007 |
| Meta-epidemiology (narrow) | 0.004 | 0.007 |
| Meta-epidemiology (broad) | 0.002 | 0.009 |
| Bibliometrics | 0.002 | 0.006 |
| Science and technology studies | 0.006 | 0.008 |
| Scholarly communication | 0.004 | 0.005 |
| Open science | 0.009 | 0.008 |
| Research integrity | 0.008 | 0.008 |
| Insufficient payload (model declined to judge) | 0.448 | 0.007 |
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; both teacher heads agree on what is shown here.
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".