Static and dynamic properties of one-dimensional disordered magnetic Ising Systems
The Ising model with random nearest-neighbor couplings is studied numerically and analytically. The J's are chosen to obey the probability laws P(J)|J|-+ with 0+1, -1J0 for AF, 0J1 for F, and -1J1 for SG. Here F means ferromagnetic, AF indicates antiferromagnetic, and SG stands for spin-glass. The thermodynamic properties are evaluated for arbitrary temperature, magnetic field, and +. The dynamics is defined by a Glauber equation of motion with random hopping matrices "+(Ji,Ji-1), "-(Ji,Ji-1), and "+(Ji,Ji-1)="-1(Ji-1,Ji). We use a continued-fraction method to evaluate the quenched averaged magnetization with M as a function of time. We find that M has two components: a fast one MF that decays exponentially and a slow nonuniversal nonexponential one Mr. A new type of clusters, named " clusters, are found to be responsible for the existence of Mr, as well as the fact that P0(J) should be a continuous function of J. In the case for which the J's take only discrete values, Mr=0. This result is obtained analytically and checked numerically via a Monte Carlo simulation of the model. The appearance of Mr is found to depend strongly on initial conditions. In particular for the AF case when all spins are parallel initially Mr=0. Hysteresis loops for the F, AF, and SG cases are also obtained with the Monte Carlo method. We point out that our results for the AF case are qualitatively similar to the recent dynamic experiments on quinolinium-ditetracyanodimethanide complexes. © 1983 The American Physical Society.