Autocorrelations: Measure the autocorrelation time
over the whole simulation, and then throw away data
for at least the first 
sweeps.
Hot and cold starts:
Start from hot (random) configuration and also a cold (ordered) configuration.
When the two have converged to the same results, then the system
is equilibrated.
(But what about first order phase transitions at 
?
Usually will not get convergence ---
in fact this is a good way to look for first order transitions.)