Reply to “Comment on ‘Hole digging in ensembles of tunneling molecular magnets’ ”
Bibliographic record
Abstract
Our work has argued for a particular scaling form governing the distribution $M(\ensuremath{\xi},t)$ of magnetization over bias $\ensuremath{\xi}$, for a system of dipolar-interacting molecular spins. This form, which was found in Monte Carlo (MC) simulations, leads inevitably to a short-time form $\ensuremath{\sim}{t}^{1∕2}$ for the magnetization relaxation in the system. The authors of the Comment argue that the magnetization should decay rather as $\ensuremath{\sim}{t}^{p}$, with the exponent $p$ depending on the lattice type---and they argue this form is valid up to infinite times. They also claim that our conclusion is based on an assumed exponential dependence of the function $M(\ensuremath{\xi},t)$ on ${\ensuremath{\tau}}_{\mathit{de}}(\ensuremath{\xi})$, the effective molecular relaxation time. In fact, our results do not depend on any such dependence, which was used merely for illustrative purposes, but only on the scaling form we found. Repeating our MC simulations for different lattice types and different parameters, we always find a square root relaxation for short times. We find that the results of the Comment are flawed because they try to fit their results over far too large a range of times (including the infinite time limit, where no simple theory applies).
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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".