A ONE-DIMENSIONAL MODEL FOR NONEXPONENTIAL RELAXATION IN A SPIN GLASS OR GLASSY SYSTEM

Abstract

In this research, we have presented the phase space of the so-called spin glass or glassy systems with a one-dimensional randomly-oriented diode network (RODN) in which the bonds between the lattice points are represented with diodes and these diodes are assumed to be fully conducting in the forward biased direction, whereas they are assumed to have some constraints, in the reverse direction, depending on the temperature and/or some other external effects. Thus, a particle's conduction (or transition) probability in the reverse direction through a diode like bond, pr, can be assumed to have values between zero and one. By employing the Monte Carlo simulation technique to the diffusion of particles through this network we have explored the relaxation mechanism, and their functional forms. Our simulation data indicates that for reverse transition probability values of pr=1.0 and 0.9, the time dependence of the relaxation data is exponential, on the other hand for pr<0.2 it may be represented by either power or logarithmic time dependence. However, in general, our data can be represented by a stretched exponential time dependence, exp (-(t/τ)α), especially in the limit of long t. Here the exponent α has values in the range of 0.3≤α≤1. For α≈1, obviously, exponential time dependence is regained. The value of α≈0.3, obtained for pr→0, is very interesting, since it is almost the same as the critical exponent, 1/3, reported in the literature for the lowest occupation probability of site points spanning percolation clusters.