High-frequency magnetic field on crystal field diluted <i>S</i> = 1 Ising system: magnetic relaxation near continuous phase transition points
Bibliographic record
Abstract
Magnetization relaxation and the steady state response of the S = 1 Ising model with random crystal field to a time varying magnetic field with a frequency ω is modelled and studied here by a method that combines the statistical equilibrium theory with the theory of irreversible thermodynamics. The method offers information on the relaxation time (τ) of the system as well as the temperature (θ) and ω dependencies of the complex (AC or dynamical) susceptibility (i.e., χ(ω) = χ′(ω) − iχ″(ω)). The so-called low- and high-frequency regions are separated by τ because τ −1 → 0 as θ approaches the critical temperatures (θ c ). One can choose to keep the frequency ω fixed and observe the low-frequency behaviors followed by the high-frequency behaviors when θ → θ c . It is shown that χ(ω) exhibits different behaviors in low- and high-frequency regimes that are separated by the quantity ωτ: χ′(ω) converges to static susceptibility and χ″(ω) → 0 for ωτ ≪ 1. However, in the high-frequency region where ωτ ≫ 1, χ′(ω) vanishes and χ″(ω) displays a peak at the critical temperature (θ c ). Besides the above, the logarithm of the susceptibility components versus log(ω) is also plotted. From these plots, one plateau (a step-like) region and a shifted peak with rising temperature is observed for the real and imaginary parts, respectively.
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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 | 0.000 | 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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 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".