A relation between the thermodynamic potential and certain spectral-weight functions in mixed singlet-triplet states of a Fermi fluid with weakly attractive interaction is established. The entire thermodynamics of the system can be derived using this relation. A similar relation is also established for an assembly of spinless, interacting bosons in the ordered phase. The latter corresponds to the Kadanoff-Baym relation for the normal phase when the necessary conditions are fulfilled. Crossover scaling forms for the susceptibility and the deviation of pressure from its critical value for the Bose system are calculated using the established relation. These forms are in general agreement with those obtained earlier by renormalization-group approaches to the problem.

• Received 18 August 1993

DOI:https://doi.org/10.1103/PhysRevB.49.1600