The transformation H ( [ R → → α α ( ν ν ) ] ) → → H ( [ ρ ρ ( x → → ) ] ) is less trivial than one might imagine and cannot be carried out exactly. The final result corresponds to the so-called random phase approximation (RPA) which has been frequently used in solid-state physics. To explicitly calculate the partition function using the segment density one has to switch to reciprocal space, change variables and only then execute the integration. For a detailed derivation see. With the partition function obtained, a variety of physical quantities can be extracted as previously described.