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arXiv · 2403.19005

The bending rigidity exponent of a two-dimensional crystalline membrane with arbitrary number of flexural phonon modes

D. A. Ivanov·A. Kudlis·I. S. Burmistrov
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Abstract

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 $\eta$ 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 $\varkappa~\sim~1/q^{\eta}$. The resulting numerical estimates of the exponent for various $d_c$ are compared with the numbers obtained from the approximate analytical techniques.

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D. A. Ivanov, A. Kudlis, I. S. Burmistrov. 2024-03-27. The bending rigidity exponent of a two-dimensional crystalline membrane with arbitrary number of flexural phonon modes. https://arxiv.org/abs/2403.19005

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