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ABSTRACT
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.
Notes
1 Harris criterion states that the introduction of randomness changes the critical phenomena of the pure system when the specific heat critical exponent is positive. Because the specific heat of the Ising model exhibits the logarithmic divergence (
) at
, the randomness does not affect the system when
. It would be expected that the stretched exponential decay is observed rather than the power-law decay in
≲ 2 since there is the crossover from the pure to the random system, whose switchover time is proportional to
.