As its name suggests, in the REM each microscopic state has an independent distribution of energy. For a particular realization of the disorder, P ( E ) = δ δ ( E − − H ( σ σ ) ) where σ σ = ( σ σ i ) refers to the individual spin configurations described by the state and H ( σ σ ) is the energy associated with it. The final extensive variables like the free energy need to be averaged over all realizations of the disorder, just as in the case of the Edwards–Anderson model. Averaging P ( E ) over all possible realizations, we find that the probability that a given configuration of the disordered system has an energy equal to E is given by