Note that after reaching equilibrium we wish to compute the mean values of several physical quantities of interest. In general this is quite time consuming and hence we do not want to calculate their values more that necessary. After a single spin flip of one spin, the values of the observables in the two configurations will not differ much, and will be almost the same. Ideally, we wish to compute the observables for configurations that are statistically independent. This means that we have to run the simulation severals steps in between measurements. This number of steps is a typical quantity that depends on the physics of the model, the parameters used, the temperature, and in particular, the ``update dynamics'' used in the algorithm, as we shall see below. This ``correlation time'' is not known a priori, and we have to estimate it with a preliminar test run.
One way to determine the time intervals over which configurations are
correlated is to compute the time-dependent autocorrelation functions
defined by: