Size-stretched exponential relaxation in a model with arrested states

Abstract

We study the effect of a rapid quench to zero temperature in a model with competing interactions, evolving through conserved spin dynamics. In a certain regime of model parameters, we find that the model belongs to the broader class of kinetically constrained models, however, the dynamics is different from that of a glass. The system shows stretched exponential relaxation with the unusual feature that the relaxation time diverges as a power of the system size. Explicitly, we find that the spatial correlation function decays as exp(−2r/L) as a function of spatial separation r in a system with L sites in the steady state, while the temporal autocorrelation function follows exp[−(t/τL)1/2], where t is the time and τL proportional to L. In the coarsening regime, after time tw, there are two growing length scales, namely L(tw)∼tw1/2 and R(tw)∼tw1/4; the spatial correlation function decays as exp[−r/R(tw)]. Interestingly, the stretched exponential form of the autocorrelation function of a single typical sample in the steady state differs markedly from that averaged over an ensemble of initial conditions resulting from different quenches; the latter shows a slow power-law decay at large times.