Some exact results for the 2D Ising model with regular disposition of the frustrated squares

Exact expressions for the free energy are derived for some regular 2D Ising models with frustrated squares. The existence of the phase transition depends on the mutual disposition of the frustrated squares. The conditions for the appearance of the phase transition in such systems are discussed. It is shown that the calculation of the partition function of the random 2D Ising model is reduced to the calculation of the determinant.