Cluster Method of Constructing Bethe Approximation for the Ising Model of a Dilute Magnet

The paper offers an interpretation of Bethe approximation based on comparison of spin clusters of different sizes on the Cayley tree. Based on this interpretation, the authors suggested the method to construct Bethe approximation for the node- or bond-diluted Ising magnet. The method provides an accurate value of the percolation threshold for the Bethe lattice. For different variations of this method, the authors constructed spontaneous magnetizations at zero and final temperatures as a function of concentration of magnetic atoms and found an analytical expression for the critical indicator of the correlation length.