Dynamics of a one-dimensional ‘‘glass’’ model: Ergodicity and nonexponential relaxation

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Abstract
We study numerically the dynamical behavior of a chain of classical particles with competing and anharmonic interactions. Although this model possesses a complex potential-energy landscape with exponentially many metastable configurations, we find ergodic behavior at all temperatures we investigated. Ergodicity is tested with respect to several correlation functions of pseudospins, the spins describing the configurational degrees of freedom of the chain. The time dependence of the autocorrelation function is consistent with a stretched exponential for intermediate times with exponents between 0.6 and 0.75. The corresponding relaxation times fit very well with an Arrhenius law. Within a transition-state approach, it is shown that the relaxation dynamics can be described by a kinetic Ising model. The consequence of this result on the autocorrelation function and the central peak is discussed.