Nonergodic dynamics of the two-dimensional random-phase sine-Gordon model: Applications to vortex-glass arrays and disordered-substrate surfaces

The dynamics of the random-phase sine-Gordon model, which describes two-dimensional vortex-glass arrays and crystalline surfaces on disordered substrates, is investigated using the self-consistent Hartree approximation. The fluctuation-dissipation theorem is violated below the critical temperature Tc for large time t>t* where t* diverges in the thermodynamic limit. While above Tc the averaged autocorrelation function diverges as Tln(t), for Tt* the dynamics becomes nonergodic. The static correlations behave as ∼Tln|rvec x| for T>Tc and for Tξ*, they behave as ∼m-1Tln|rvec x| where m∼T/Tc near Tc, in general agreement with the variational replica-symmetry breaking approach and with recent simulations of the disordered-substrate surface. For strong coupling the transition becomes first order