The bending rigidity exponent of a two-dimensional crystalline membrane with arbitrary number of flexural phonon modes
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866910388348518400 |
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| author | Ivanov, D. A. Kudlis, A. Burmistrov, I. S. |
| author_facet | Ivanov, D. A. Kudlis, A. Burmistrov, I. S. |
| contents | We investigate the elastic behavior of two-dimensional crystalline membrane embedded into real space taking into account the presence an arbitrary number of flexural phonon modes $d_c$ (the number of out-of-plane deformation field components). The bending rigidity exponent $η$ is extracted by numerical simulation via Fourier Monte Carlo technique of the system behaviour in the universal regime. This universal quantity governess the correlation function of out-of-plane deformations at long wavelengths and defines the behaviour of renormalized bending rigidity at small momentum $\varkappa~\sim~1/q^η$. The resulting numerical estimates of the exponent for various $d_c$ are compared with the numbers obtained from the approximate analytical techniques. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_19005 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The bending rigidity exponent of a two-dimensional crystalline membrane with arbitrary number of flexural phonon modes Ivanov, D. A. Kudlis, A. Burmistrov, I. S. Statistical Mechanics We investigate the elastic behavior of two-dimensional crystalline membrane embedded into real space taking into account the presence an arbitrary number of flexural phonon modes $d_c$ (the number of out-of-plane deformation field components). The bending rigidity exponent $η$ is extracted by numerical simulation via Fourier Monte Carlo technique of the system behaviour in the universal regime. This universal quantity governess the correlation function of out-of-plane deformations at long wavelengths and defines the behaviour of renormalized bending rigidity at small momentum $\varkappa~\sim~1/q^η$. The resulting numerical estimates of the exponent for various $d_c$ are compared with the numbers obtained from the approximate analytical techniques. |
| title | The bending rigidity exponent of a two-dimensional crystalline membrane with arbitrary number of flexural phonon modes |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2403.19005 |