Mean field theory of a quantum Heisenberg spin glass

A full mean-field solution of a quantum Heisenberg spin-glass model is pres ented in a large-N limit. A spin-glass transition is found for all values o f the spin S. The quantum critical regime associated with the quantum trans ition at S = 0 and the various regimes in the spin-glass phase at high spin are analyzed. The specific heat is shown to vanish linearly with temperatu re. In the spin-glass phase, intriguing connections between the equilibrium properties of the quantum problem and the out-of-equilibrium dynamics of c lassical models are pointed out.