  Effects of the averaging over disorder realizations (samples) on the phase
behavior are analyzed in terms of the mean field approximation for the random
field Ising model with infinite range interactions. It is found that the
averaging is equivalent to a drastic modification in the statistics of the
quenched variables. In its turn, this lowers the critical temperature of a
second-order phase transition or, depending on the sampling, even suppresses
the ordered phase. Possible first order transitions are shown to be softened by
the sample averaging. Common issues and differences in the interpretation of
these effects in the context of the simulation and experimental studies are
discussed.
