The m -component spin glass on a Bethe lattice

We study the m -component vector spin glass in the limit m→∞ on a Bethe lattice. The cavity method allows for a solution of the model in a self-consistent field approximation and for a perturbative solution of the full problem near the phase transition. The low-temperature phase of the model is analyzed numerically and a generalized Bose-Einstein condensation is found, as in the fully connected model. Scaling relations between four distinct zero-temperature exponents are found.