  We investigate an XY spin-glass model in which both spins and interactions
(or couplings) evolve in time, but with widely separated time-scales. For large
times this model can be solved using replica theory, requiring two levels of
replicas, one level for the spins and one for the couplings. We define the
relevant order parameters, and derive a phase diagram in the replica-symmetric
approximation, which exhibits two distinct spin-glass phases. The first phase
is characterized by freezing of the spins only, whereas in the second phase
both spins and couplings are frozen. A detailed stability analysis leads also
to two distinct corresponding de Almeida-Thouless lines, each marking
continuous replica-symmetry breaking. Numerical simulations support our
theoretical study.
