Before taking measurements, we must be sure that the Markov process has thermalized, or reached equilibrium, i.e. and the arbitrary initial configuration has been ``forgotten.''
Approach to equilibrium is exponential . The autocorrelation time can be very large. May thermalize for 100,000 sweeps at a certain T, but if is of the same order, then the measurements are suspect.
There are 3 main techniques for checking for thermalization:
Binning: Check to see whether measurements are converging to a constant average value. Can do this by binning the data, i.e. splitting measurements up into a number of large contiguous segments ( bins). Averages are taken over each bin, and data from initial deviant bins is discarded. Binning can also be used to calculate errors (see later).