  The short-time critical dynamics of propagation of damage in the Ising
ferromagnet in two dimensions is studied by means of Monte Carlo simulations.
Starting with equilibrium configurations at $T= \infty$ and magnetization
$M=0$, an initial damage is created by flipping a small amount of spins in one
of the two replicas studied. In this way, the initial damage is proportional to
the initial magnetization $M_0$ in one of the configurations upon quenching the
system at $T_C$, the Onsager critical temperature of the
ferromagnetic-paramagnetic transition. It is found that, at short times, the
damage increases with an exponent $\theta_D=1.915(3)$, which is much larger
than the exponent $\theta=0.197$ characteristic of the initial increase of the
magnetization $M(t)$. Also, an epidemic study was performed. It is found that
the average distance from the origin of the epidemic ($\langle R^2(t)\rangle$)
grows with an exponent $z^* \approx \eta \approx 1.9$, which is the same,
within error bars, as the exponent $\theta_D$. However, the survival
probability of the epidemics reaches a plateau so that $\delta=0$. On the other
hand, by quenching the system to lower temperatures one observes the critical
spreading of the damage at $T_{D}\simeq 0.51 T_C$, where all the measured
observables exhibit power laws with exponents $\theta_D = 1.026(3)$, $\delta =
0.133(1)$, and $z^*=1.74(3)$.
