The XY Spin-Glass with Slow Dynamic Couplings

Details The XY Spin-Glass with Slow Dynamic Couplings The XY Spin-Glass with Slow Dynamic Couplings

1998-07-06

arxiv.org/abs/cond-mat/9807082v1

J.Phys.A 31 (1998), L737-L742

Physics

Condensed Matter

Disordered Systems and Neural Networks

7 pages, Latex, 3 eps figures

Scientific paper

10.1088/0305-4470/31/44/002

We investigate an XY spin-glass model in which both spins and couplings evolve in time: the spins change rapidly according to Glauber-type rules, whereas the couplings evolve slowly with a dynamics involving spin correlations and Gaussian disorder. For large times the model can be solved using replica theory. In contrast to the XY-model with static disordered couplings, solving the present model requires two levels of replicas, one for the spins and one for the couplings. Relevant order parameters are defined and a phase diagram is obtained upon making the replica-symmetric Ansatz. The system exhibits two different spin-glass phases, with distinct de Almeida-Thouless lines, marking continuous replica-symmetry breaking: one describing freezing of the spins only, and one describing freezing of both spins and couplings.

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