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

2024/03/27 by Д. А. Иванов, Ivanov, D. A., A. Kudlis +3
Engineering · #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #Structural Analysis and Optimization

paper · pdf · doi:10.48550/arxiv.2403.19005

openalex publication_date 2024/03/27 · openalex created_date 2024/03/30 · openalex updated_date 2026/07/28

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 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~∼~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.

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