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

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 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 ϰ∼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.