Thus, equations 1 and 2 need to be solved self-consistently, to obtain the free energy values, fm for each value of T. Using these free energies, the density of states and average properties (i.e., E ) are then calculated from the following expressions:

(3)

and the average quantity of an observable, A , is then calculated as

(4)

From the DOS, we obtain the partition function, Z , as:

Figure 9.4: Schematic representation of energy histogram, H(E) for temperature ranges from T₁ to T₁₀.