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 ${\theta }_D=1.915\left(3\right)$, which is much larger than the exponent $\theta =0.197$ characteristic of the initial increase of the magnetization $M\left(t\right)$. Also, an epidemic study was performed. It is found that the average distance from the origin of the epidemic $\left(⟨R^2\left(t\right)⟩\right)$ grows with an exponent $z^{\ast }\approx \eta \approx 1.9$, 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 $T_D\simeq 0.51T_C$, where all the measured observables exhibit power laws with exponents ${\theta }_D=1.026\left(3\right)$, $\delta =0.133\left(1\right)$, and $z^{\ast }=1.74\left(3\right)$.

• Received 9 February 2010

DOI:https://doi.org/10.1103/PhysRevE.81.051116