Spherical model on the Cayley tree

Abstract

We investigate the phase transition of the spherical model on the Cayley tree. There is only one transition temperature T,; the specific heat shows a finite discontinuity at Tc; there is no spontaneous magnetisation; the susceptibility remains finite, but shows a cusp at Tc with infinite slope on the high temperature side. These results differ significantly from spherical model properties on a lattice and from the recent Ising model calculations on the Cayley tree with its phase transition of continuous order.