Phase transitions in layered spin systems

The partition function and binary correlation functions are calculated for a layered system of spins $1/2$ whose interaction within each layer is described by the Curie–Weiss model with the spins in different layers interacting only when they are nearest neighbours. The calculations are made by means of the transfer matrix method. A variant of this method is proposed that under certain conditions eliminates the need to calculate the maximal eigenvalue of this matrix.