THE XY SPIN-GLASS WITH SLOW DYNAMIC COUPLINGS

We investigate an XP spin-glass model in which both spins and coupling s evolve in time: the spins change rapidly according to Glauber-type r ules, whereas the couplings evolve slowly with a dynamics involving sp in correlations and Gaussian disorder. For large times the model can b e solved using replica theory. In contrast to the XY-model with static disordered couplings, solving the present model requires two levels o f replicas, one for the spins and one for the couplings. Relevant orde r parameters are defined and a phase diagram is obtained upon making t he replica-symmetric ansatz. The system exhibits two different spin-gl ass phases, with distinct de Almeida-Thouless lines, marking continuou s replica-symmetry breaking: one describing freezing of the spins only , and one describing freezing of both spins and couplings.