Accounting for the ultraviolet divergence in field-theoretic simulations of block copolymer melts
Bibliographic record
Abstract
This study examines the ultraviolet (UV) divergence in field-theoretic simulations (FTSs) of block copolymer melts, which causes an unphysical dependence on the grid resolution, Δ, used to represent the fields. Our FTSs use the discrete Gaussian–chain model and a partial saddle-point approximation to enforce incompressibility. Previous work has demonstrated that the UV divergence can be accounted for by defining an effective interaction parameter, χ=z∞χb+c2χb2+c3χb3+⋯, in terms of the bare interaction parameter, χb, used in the FTSs, where the coefficients of the expansion are determined by a Morse calibration. However, the need to use different grid resolutions for different ordered phases generally restricts the calibration to the linear approximation, χ ≈ z∞χb, and prevents the calculation of order–order transitions. Here, we resolve these two issues by showing how the nonlinear calibration can be translated between different grids and how the UV divergence can be removed from free energy calculations. By doing so, we confirm previous observations from particle-based simulations. In particular, we show that the free energy closely matches self-consistent field theory (SCFT) predictions, even in the region where fluctuations disorder the periodic morphologies, and similarly, the periods of the ordered phases match SCFT predictions, provided the SCFT is evaluated with the nonlinear χ.
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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 | 0.001 | 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 | 0.001 | 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".