Coupled dynamics of fast spins and slow exchange interactions in the XY spin-glass

Details Coupled dynamics of fast spins and slow exchange interactions in the XY spin-glass Coupled dynamics of fast spins and slow exchange interactions in the XY spin-glass

2000-11-03

arxiv.org/abs/cond-mat/0011065v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

30 pages, 15 figures, LaTeX (J. Phys. A style)

Scientific paper

10.1088/0305-4470/34/19/302

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.

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