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Anomalous criticality coexists with giant cluster in the uniform forest model
by Hao Chen, Jesús Salas, Youjin Deng
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Hao Chen · Youjin Deng · Jesús Salas |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2309.17210v2 (pdf) |
| Date accepted: | 2024-04-26 |
| Date submitted: | 2024-04-03 10:26 |
| Submitted by: | Chen, Hao |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Computational |
Abstract
We show by extensive simulations that the whole supercritical phase of the three-dimensional uniform forest model simultaneously exhibits an infinite tree and a rich variety of critical phenomena. Besides typical scalings like algebraically decaying correlation, power-law distribution of cluster sizes, and divergent correlation length, a number of anomalous behaviors emerge. The fractal dimensions for off-giant trees take different values when being measured by linear system size or gyration radius. The giant-tree size displays two-length scaling fluctuations, instead of following the central-limit theorem.
List of changes
1. Expand the "Theoretical Insights" section, and move it before the "Results" section.
2. Fix the typo in the title: "...giant clusterin ..." -> "... giant cluster in ...".
3. Add a definition of the off-giant correlation $g^\prime(r)$ in the third paragraph of the "Introduction" section.
4. Fix the text overfull on the first line of the abstract.
5. Fix the text overfull in the "Fits" section related to the definition of the susceptibility.
Published as SciPost Phys. 16, 121 (2024)
Reports on this Submission
Report #2 by Anonymous (Referee 1) on 2024-4-5 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2309.17210v2, delivered 2024-04-05, doi: 10.21468/SciPost.Report.8829
Strengths
1- broad interest of the investigated model
2- solid numerical approach
3- interesting numerical results
Report
The authors study the percolative properties of the supercritical phase for the 3D uniform forest (i.e. arboreal gas) model. This system has similarities with the Potts model, but is characterized by a continuous (rather than discrete) symmetry, and to the N-vector model, analytically continued to N=−1.
They study the Fourier-transformed susceptibility and off-giant correlation to show the fractalization of the off-giant cluster and their critical scaling behaviour. The system is simulated by the Sweeny algorithm for a simple-cubic lattice up to size 128^3.
Even though a full theoretical comprehension of their results is missing, the numerical approach is solid and the results are sound and interesting. Surely, the results obtained by the authors, and the implemented approach, are of broad interest due the relation existing between the uniform forest model and other statistical mechanics and condensed-matter physics systems.
Therefore, I recommend publication of the manuscript in SciPost Physics in its current form.