INFINITE-RANGE-INTERACTION M-COMPONENT QUANTUM SPIN-GLASSES - STATICS AND DYNAMICS IN THE LARGE-M LIMIT

The infinite-range M-component models of quantum rotors and anharmonic oscillators coupled by random exchange interactions with Gaussian distributions are considered. Both models exhibit a quantum phase transition separating the spin-glass and disordered phases where the quantum effects are regulated by a parameter DELTA (inverse momentum of inertia for rotor model and inverse mass for oscillator model) parametrizing the kinetic energy. The models allow, in the limit M --> infinity, for an exact solution in both the spin-glass and disordered phases. Employing the quantum finite-temperature real-time description, we examine the static and dynamic properties of the systems without making use of the n-replica method. We find that the dynamical solution is marginally stable in the spin-glass phase with a constant static susceptibility below the spin-glass freezing temperature. A closed-form solution for the averaged free energy has been obtained and various thermodynamic functions are derived. In particular, the entropy is always positive in the spin-glass phase and goes to zero with a T3 dependency in the low-temperature region. This is in contrast to the classical M-component Heisenberg model in the M --> infinity limit.