Non-Ergodic Dynamics of the 2D Random-phase Sine-Gordon Model: Applications to Vortex-Glass Arrays and Disordered-Substrate Surfaces

Abstract

The dynamics of the random-phase sine-Gordon model, which describes 2D 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 T_c for large time t>t* where t* diverges in the thermodynamic limit. While above T_c the averaged autocorrelation function diverges as Tln(t), for T t*) where νis a temperature-dependent exponent. On larger time scales t > t* the dynamics becomes non-ergodic. The static correlations behave as Tln{x} for T>T_c and for T ξ*, they behave as (T/m)ln{x} where m is approximately T/T_c near T_c, 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.