Once the relevant physical quantities (energy, superfluid and
condensate fraction) have been calculated for a given configuration
of disorder, the simulation is repeated for different
configurations and finally the average over disorder
configurations is taken.
As the computation for a given disorder configuration is heavy and
it takes a lot of time to complete the runs with different
configurations, it is very important to understand the behavior of
the statistical error due to the average over realizations. The
results for the energy are shown in Fig. 4.2.
Figure 4.2:
The average of the energy over disorder as a function of the
bumber of different disorder realizations. The error bars show the
variance of the averaging.
Fortunately, energy and the other quantities converge very rapidly
to the mean value. Due to the self-averaging 5 or 6 disorder
configurations are enough for most of the cases.