2 A solvable spin glass of quantum rotors

A solvable spin glass of quantum rotors. We examine a model of M-component quantum rotors coupled by Gaussian-distributed random, infinite-range exchange interactions. A complete solution is obtained at M = ∞ in the spin-glass and quantum-disordered phases. The quantum phase transition separating them is found to possess logarithmic violations of scaling, with no further modifications to the leading critical behavior at any order in 1/M ; this suggests that the critical properties of the transverse-field Ising model (believed to be identical to the M → 1 limit) are the same as those of the M = ∞ quantum rotors.