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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).

Paul Coddington, Northeast Parallel Architectures Center at Syracuse University,