  We have investigated the time evolution of the vacancy-mediated disordering
process in binary alloys at finite temperatures. Qualitatively, we monitor the
changes in the configurations by taking sequences of snapshots for various
temperatures and comparing their morphologies. Quantitatively, we carry out
Monte Carlo simulations to determine the time-dependent disorder parameter
A(L;T;t) and the time-dependent structure factors Sk(t) for moderately low
temperatures. This study differs from previous studies done at infinite
temperature in that the vacancy here executes highly active walks, which are
subjected to nonlinear feedbacks, instead of the random walks that take place
in the limit of T ->infinity. We find that the slope of the log-log plot of
A(L; T; t) vs. t for finite temperatures follows the temperature dependence
given by the Gompertz function and reaches a limiting value of 1/2 only as the
temperature approaches infinity. For the structure factors, namely, Sk(t) vs.
t, the overall features are similar to those found at infinite T. The two key
differences between our results and those at infinite T are the saturated value
and the intermediate region in which the portion of the graph whose slope is
equal to one becomes smaller and is gradually replaced by a curve having a
slope of 0.5. This last difference is especially evident at very low
temperatures.
