Resonances in the generalized $LC$ model of granular metal–dielectric nanocomposites

$LC$ networks in the form of spatial lattices with randomly arranged inductive and capacitive bonds, which serve as an adequate theoretical model for describing plasmon resonances in disordered granular metal–dielectric composites, have been considered. Earlier, such networks were theoretically studied only in the case when the values of all $L$- and $C$-bonds were equal. This approximation is not applicable when the sizes of metallic granules and dielectric gaps between them appreciably fluctuate. In the present work, a generalized model making it possible to consider networks with arbitrary values of $L$ and $C$ is developed. Using this generalized model, the spectral density of resonant states for networks with different values of inductive and capacitive bonds is studied. It is shown that, in the case of a discrete set of values of $L$- and/or $C$-bonds, the typical peaks in the density of states are split and, in the case of a continuous distribution of these values, they are smoothened. Anticrossing of frequencies due to dipole–dipole interaction of single resonant clusters is studied, and a logarithmic singularity in the spectral state density at the ends of the spectrum for smooth distributions of $L$ and $C$ is found.