Relaxational processes in the one-dimensional diluted Ising model with long-range interactions are numerically investigated. When the dilution is relevant, the power-law decay of autocorrelation functions is observed as the droplet theory predicts. The power-law decay is expected to disappear in the high dimensional mean-field ordered phase and in the low dimensional Kosterlitz-Thouless phase. Numerical results, however, show that the power-law decay survives in the mean-field ordered phase, and nontrivial stretched exponential decay is observed at the lower critical dimension.
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