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The dynamics of the random-phase sine-Gordon model, which describes 2Dvortex-glass arrays and crystalline surfaces on disordered substrates, isinvestigated using the self-consistent Hartree approximation. Thefluctuation-dissipation theorem is violated below the critical temperature T_cfor large time t>t* where t* diverges in the thermodynamic limit. While aboveT_c the averaged autocorrelation function diverges as Tln(t), for T<T_c itapproaches a finite value q* proportional to 1/(T_c-T) as q(t) = q* -c(t/t*)^{-\nu} (for t --> t*) where \nu is a temperature-dependent exponent. Onlarger time scales t > t* the dynamics becomes non-ergodic. The staticcorrelations behave as Tln{x} for T>T_c and for T<T_c when x < \xi* with \xi*proportional to exp{A/(T_c-T)}. For scales x > \xi*, they behave as (T/m)ln{x}where m is approximately T/T_c near T_c, in general agreement with thevariational replica-symmetry breaking approach and with recent simulations ofthe disordered-substrate surface. For strong- coupling the transition becomesfirst-order.Comment: 12 pages in LaTeX, Figures available upon request, NSF-ITP 94-10

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