EXACT SOLUTION OF THE ISING-MODEL ON CHECKERBOARD FRACTALS IN AN EXTERNAL MAGNETIC-FIELD

In this paper we use a diagrammatic technique to determine the exact r ecursion relations for the partition function of the Ising model in an external magnetic field, situated on the first two members of the che ckerboard family of fractal lattices embedded in two dimensions. This represents the first exact general solution of this model for the case of nonzero field. The closed-form expression for the partition functi on is obtained for the first member in the zero-field limit and the no nzero-field recursion relations prove sufficient for exact evaluation of the response functions. We also calculate the temperature dependenc e of the specific heat and susceptibility.