Abstract
The authors consider a fully frustrated Ising model on a square lattice, depending on four parameters. The partition function is shown to be equivalent to the two-parameter (ferromagnetic) Onsager partition function. This result generalises a relation established by Southern et al. (1980), and can be checked in the particular case of the (one-parameter) Villain model. In particular, the residual entropy of the Villain model is linked to the free energy of the Onsager model at criticality. The reduction from four to two parameters, occurring in this mapping, is studied in the light of the inverse relation satisfied by the partition function of the frustrated model.