Spherical Model as the Limit of Infinite Spin Dimensionality

The Berlin-Kac spherical model (or"spherical approximation to the Ising model") H^SM=-J〈ij〉₈₉, with j=1{u₉}^2=N, is found to be equivalent to the limit of the Hamiltonian H^ () =-J〈ij〉{S₈}^ () {S₉}^ (), where {S₈}^ () are isotropically interacting -dimensional classical spins.