SciPost Submission Page
Universal and non-universal large deviations in critical systems
by Ivan Balog, Bertrand Delamotte and Adam Ran\c con
Submission summary
| Authors (as registered SciPost users): | Ivan Balog |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202410_00005v1 (pdf) |
| Date submitted: | 2024-10-02 10:53 |
| Submitted by: | Balog, Ivan |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
Rare events play a crucial role in understanding complex systems. Characterizing and analyzing them in scale-invariant situations is challenging due to strong correlations. In this work, we focus on characterizing the tails of probability distribution functions (PDFs) for these systems. Using a variety of methods, perturbation theory, functional renormalization group, hierarchical models, large $n$ limit, and Monte Carlo simulations, we investigate universal rare events of critical $O(n)$ systems. Additionally, we explore the crossover from universal to nonuniversal behavior in PDF tails, extending Cramér's series to strongly correlated variables. Our findings highlight the universal and nonuniversal aspects of rare event statistics and challenge existing assumptions about power-law corrections to the leading stretched exponential decay in these tails.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Reports on this Submission
Strengths
Scientifically sound, clearly written, of interest to theoretical community, different analytic and numerical methods, exceptional quality of numerical data.
Weaknesses
Lacking some background for the non-expert reader, absence of consequences for experiment
Report
This is an interesting and generally well written paper addressing the statistical properties of spatially averaged variables in the large deviation range of fluctuations, with particular reference to order parameter fluctuations at thermodynamic equilibrium and near a second order phase transition. I think that it could make a valid contribution to Sci Post and I recommend it's publication. Some points to be considered before publication are included below.
Requested changes
1. One thing I have noted is that the exponents used in the analysis, beta/nu, delta, eta depend uniquely on the eigenvalue exponent y_h related to the field variable. I think this is because of the particular choice of order parameter fluctuations at T=T_c and small field. If one studied fluctuations of the enthalpy, H=U-Nhm, even at T=T_c, the critical scaling would involve y_t as well as y_h. Or, for the order parameter, working at zero field, with reduced temperature t would (I think) introduce the second exponent, y_t through the critical exponent nu. Could this be done ? Is it of interest ? Or does it just add complexity without content ?
2. I was a bit confused about some of the universality classes appearing in the analysis. In particular for the hierarchical model, I was expecting a tree calculation to yield mean field critical exponents but the expression seems to predict delta=5. Is that correct ? It is quite close to the D=3 value but I don't see dimensionality in the hierarchy. In addition to referencing [22] it would be worthwhile discussing this in the text.
3. Similarly, it would be useful to be reminded what one can expect in the large n limit. Naively I was again expecting mean field exponents, but we have 2beta/nu=d-1 and delta=2d/(d-2). References would be useful. These expressions predict unexpected results for d=4.
4. I appreciated the discussion of finite size effects and the consequences for entering the universal large deviation regime in d=2 and d=3. Does this mean that experimentally the regime might just be accessible in d=3 ? What about systems like helium-4 where the lambda transition can be approached with exquisite precision and where finite size effects such as the critical Casimir force can be measured ?
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)