The ground state of a spin glass

Abstract

The classical model of a spin glass, consisting of dipoles arranged in random positions and experiencing random forces is directly quantised assuming the dipoles have a moment of inertia I. The ground state of this system presents a similar problem to that of the thermal behaviour of the classical system in that quantum fluctuations compete with the potential energy of the system. It is shown that a spin glass exists provided that the dimensionless parameter J₀I/h² is greater than a critical value, where NJ₀ is the classical ground state energy and N the number of dipoles. When the parameter is less than this value the ground state is not a spin glass, the dipoles being approximately in s states so that no spin glass can exist.