EXACT ZERO-FIELD SUSCEPTIBILITY OF THE ISING-MODEL ON A CAYLEY TREE

We establish an exact expression, in closed form, for the zero-field s usceptibility of the Ising model on a Cayley tree of arbitrary generat ion. We use the known exact recursion relations for the partition func tion to find the corresponding recursion relations for its field deriv atives. These relations are then iterated for the zero-held case to yi eld the expression for the zero-field susceptibility. In the thermodyn amic limit, our formula displays behavior in agreement with previous w orks. (C) 1998 Elsevier Science B.V. All rights reserved.