A disordered spin model with a quantum-induced phase transition related to Bose condensation in a random potential

Abstract

The authors consider a random magnetic model which is related to Bose condensation in the presence of a random potential. It is an XY model with a random z field. The classical model always has an ordered ground state. The nature of the ground state is unusual: the main contribution to the spontaneous magnetisation comes from a dilute set of weakly interacting pairs of spins. Within each pair the spins are strongly coupled, so for low-energy dynamics only the motion of the total spin of the pair is relevant. This allows the construction of an effective Hamiltonian only involving the pairs' total spins. When this is semi-classically quantised via a 1/S expansion, they find that the zero-point spin wave motion destroys the magnetised ground state if either the number of spin states is sufficiently small (for fixed strength of disorder), or for sufficiently large disorder (for fixed number of spin states). Finally they discuss the relation of the model to the problem of Bose condensation in a random potential, where the interaction strength is related to the number of spin states in the spin model.