After some consideration the Hamiltonian of equation 8.1 was taken for consideration with 
a constant, i.e. isotropic
in both spin and space dimensions, infinite space dimension, i.e. every spin interacting equally with every other spin, a spin dimension of three, i.e. Heisenberg spins, and zero external field. This is analogous to the Sherrington-Kirkpatrick (SK) model (infinite space dimension) [45], but the interaction strength in the SK case is taken as a site-random quantity and the spins are Ising, which implies that the SK analysis is necessarily classical. Thus the Hamiltonian of interest is
When this Hamiltonian is written, as below, in terms of the total spin 
and the individual spins then the eigenstates are immediately seen to be those where the system total and individual angular momentum j values are listed.
