The integrated autocorrelation times for an observable X are obtained using the method proposed by Sokal [4,5], namely
with
and m chosen so that 
. The smallest value of m
for which 
has been chosen in a self-consistent
manner. From here we derive an estimate for the error of 
given
by the formula
We call this criterion -- ``criterion 
''.
We also double check our results against the procedure employed by the QCD-TARO Collaboration [6], wherein the autocorrelation time is defined as:
where N is determined so that 
is maximized, but 
of the total sample and 
. Likewise, we call this
criterion -- ``criterion 
''.
We use hybrid overrelaxation updating scheme, which is considered to be the
state-of-the-art algorithm for bosonic systems when no cluster algorithm is
available [7]. It simply consists in the mixing of Cabibbo-Marinari
pseudo-heatbath and the Brown-Woch microcanonical overrelaxation sweeps with a
ratio 
[8,9].