Short-Time Critical Dynamics of Damage Spreading in the Two-Dimensional Ising Model

M. LETICIA RUBIO PUZZO; EZEQUIEL V. ALBANO

PHYSICAL REVIEW E - STATISTICAL PHYSICS, PLASMAS, FLUIDS AND RELATED INTERDISCIPLINARY TOPICS

APS Journal

Lugar: Nueva York; Año: 2010 vol. 81 p. 511161 - 511167

1063-651X

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 ($<R^2(t)>$) 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 $z*=1.74(3)$.