2D hex, soft sphere, disordered system density of states

For my most disordered system (gamma=1.0), I assembled the covariance matrix for 4 million steps and diagonalized it for its eigenvalues. This system has 4200 particles. The plot above shows the convergence of 1/eigenvalues for various sampling intervals.

The plot below shows the convergence of histograms of the eigenvalues plotted above.



In the plot above, I have shown the DOS of various window sizes (shown in the legend). All eigenvalues were obtained by diagonalizing the covariance matrix obtained after sampling 4 million steps. For small frequencies, we expect linear DOS. Note the bimodal nature of the DOS. For comparison, below is a plot of the ordered (gamma=0.0) system's DOS.