We study a model system composed of interacting quantum spins, with every spin coupled to every other, in the limit where the number of spins K and the angular momentum j of each spin are both large, aiming to explore the effect of large system size on the breakdown of the classical limit of quantum mechanics. We obtain the exact spectrum of the Hamiltonian, and hence the trace of the quantum-mechanical time-evolution operator. We examine the time dependence of , finding a simple approximation which is valid when j and K are large. At a time proportional to , this approximation breaks down, and the long-time behaviour is extremely complex. We use a renormalization scheme to investigate this complexity. The scheme is based upon a generalization of the Gauss continued-fraction map to the complex plane.