Dispersion dependencies of dielectric properties. Renormgroup approach

The ac dielectric response of metal-insulator composites is studied numerically, using renormgroup's algorithm. For 2D and 3D random composites with bond percolation, we verify numerically that the effective dielectric function can be written numerically in the form epsilon(e)/epsilon(1) = xi(-tau/v), G((epsilon(2)/epsilon(1)) xi((tau + s)/v), xi/L, where (epsilon)over dot (2) and epsilon (1) are the dielectric functions, xi is the correlation length, L is the system size (or wavelength of the electric field), G - universal functions above and below percolation, t, s and v are standard percolation exponents. A similar form has been previously verified (or bond percolation) by Bug et al. We have used a random resistor - capacitor network as a representation of a metal-insulator composite near the percolation threshold, and have calculated the scaling function using a real-space renormalization-group approach. The main idea of such approach consists of step-by-step averaging on levels of hierarchical lettice,This process is continued to fixed point of dielectric's concentration. We are finding the concentration dependencies of effective characteristics of composite material for different initial concentration of dielectric in spread range of frequencies.