Using Monte Carlo simulation on the simplest possible statistical mech
anical model, the two-dimensional, nonconserved kinetic Ising model th
at undergoes an order-disorder transition, we show that the local orde
r of the ordering domains, subsequent to a temperature quench, transie
ntly overshoots the value of the equilibrium order parameter. It is ar
gued that overshooting is a generic effect in ordering dynamics, indep
endent of the detailed dynamics and the conservation laws in effect.