One important issue must be considered when using the metropolis algorithm with the canonical distribution: when performing a given measure, i.e. realization of r → → i , one must ensure that that realization is not correlated with the previous state of the system (otherwise the states are not being "randomly" generated). On systems with relevant energy gaps, this is the major drawback of the use of the canonical distribution because the time needed to the system de-correlate from the previous state can tend to infinity.