Dynamical renormalization group analysis of $O(n)$ model in steady shear flow
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arXiv
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| Format: | Preprint |
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2024
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| author | Ikeda, Harukuni Nakano, Hiroyoshi |
| author_facet | Ikeda, Harukuni Nakano, Hiroyoshi |
| contents | 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 $d = 2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_02111 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dynamical renormalization group analysis of $O(n)$ model in steady shear flow Ikeda, Harukuni Nakano, Hiroyoshi Statistical Mechanics Soft Condensed Matter 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 $d = 2$. |
| title | Dynamical renormalization group analysis of $O(n)$ model in steady shear flow |
| topic | Statistical Mechanics Soft Condensed Matter |
| url | https://arxiv.org/abs/2412.02111 |