  We describe a method to study the rate at which modes decorrelate in
numerical simulations. We study the XY model updated with the Metropolis and
Wolff dynamics respectively and compute the rate at which each eigenvector of
the dynamics decorrelates. Our method allows us to identify the decorrelation
time for each mode separately. We find that the autocorrelation function of the
various modes is markedly different for the `local' Metropolis compared to the
`non-local' Wolff dynamics. Equipped with this new insight, it may be possible
to devise highly efficient algorithms.
