  Dynamics of ordering in Ising model, following quench to zero temperature,
have been studied via Glauber spin-flip Monte Carlo simulations in space
dimensions $d=2$ and $3$. One of the primary objectives has been to understand
phenomena associated with the persistent spins, viz., time decay in the number
of unaffected spins, growth of the corresponding pattern and its fractal
dimensionality, for varying correlation length in the initial configurations,
prepared at different temperatures, at and above the critical value. It is
observed that the fractal dimensionality and the exponent describing the
power-law decay of persistence probability are strongly dependent upon the
relative values of nonequilibrium domain size and the initial equilibrium
correlation length. Via appropriate scaling analyses, these quantities have
been estimated for quenches from infinite and critical temperatures. The above
mentioned dependence is observed to be less pronounced in higher dimension. In
addition to these findings for the local persistence, we present results for
the global persistence as well. Further, important observations on the standard
domain growth problem are reported. For the latter, a controversy in $d=3$,
related to the value of the exponent for the power-law growth of the average
domain size with time, has been resolved.
