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 behavior in the universal regime. This universal quantity governs the correlation function of out-of-plane deformations at long wavelengths and defines the behavior 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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• Membranes
• Phonons
• Critical exponents
• Monte Carlo methods