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Dynamical renormalization group analysis of $O(n)$ model in steady shear flow
by Harukuni Ikeda, Hiroyoshi Nakano
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Harukuni Ikeda |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2412.02111v1 (pdf) |
| Date submitted: | Dec. 18, 2024, 6:16 a.m. |
| Submitted by: | Harukuni Ikeda |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We study the critical behavior of the $O(n)$ model under steady shear flow using a dynamical renormalization group (RG) method. Incorporating the strong anisotropy in scaling ansatz, which has been neglected in earlier RG analyses, we identify a new stable Gaussian fixed point. This fixed point reproduces the anisotropic scaling of static and dynamical critical exponents for both non-conserved (Model A) and conserved (Model B) order parameters. Notably, the upper critical dimensions are $d_{\text{up}} = 2$ for the non-conserved order parameter (Model A) and $d_{\text{up}} = 0$ for the conserved order parameter (Model B), implying that the mean-field critical exponents are observed even in both $d=2$ and $3$ dimensions. Furthermore, the scaling exponent of the order parameter is negative for all dimensions $d \geq 2$, indicating that shear flow stabilizes the long-range order associated with continuous symmetry breaking even in $d = 2$. In other words, the lower critical dimensions are $d_{\rm low} < 2$ for both types of order parameters. This contrasts with equilibrium systems, where the Hohenberg -- Mermin -- Wagner theorem prohibits continuous symmetry breaking in $d = 2$.
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
1- Novel anisotropic scaling which is consistent with the expression of the correlation function in the mean field theory under shear
2-Gaussian fixed point with non vanishing shear strength
Weaknesses
Report
The author asserts that the nontrivial fixed point proposed by Onuki and Kawasaki (OK), which is unstable under shear, does not adequately describe dynamical critical phenomena. My understanding is that, while OK acknowledged the instability of their fixed point with respect to shear, they conducted analyses around the fixed point to discuss scaling behavior under such conditions. Therefore, I feel it is necessary to provide a more detailed discussion of how and to what extent the analysis by OK is rendered invalid.
Requested changes
1- More comments on the previous work by Onuki and Kawasaki
Recommendation
Ask for minor revision
Strengths
1- interesting open problem 2-simple and clear-cut approach 3-use of standard well-known techniques 4-important result with relatively little work (new exponents at tree level!) 5-clarifies previous numerical methods and suggests why in some cases there are ambiguous numerical results (log corrections at $d_\mathrm{up}$) 6-relatively short and concise
Weaknesses
2-somewhat arbitrary choice of the scale invariant condition to fix the exponents
3-why other choices of the scaling condition give unphysical results or no solution?
Report
Recommendation
Publish (surpasses expectations and criteria for this Journal; among top 10%)