Transient Behavior of Damage Spreading in the Two-Dimensional Blume–Capel Ferromagnet

We study the transient behavior of damage propagation in the two-dimensional spin-1 Blume–Capel model using Monte Carlo simulations with Metropolis dynamics. We find that, for a particular region in the second-order transition regime of the crystal field–temperature phase diagram of the model, the average Hamming distance decreases exponentially with time in the weakly damaged system. Additionally, its rate of decay appears to depend linearly on a number of Hamiltonian parameters, namely the crystal field, temperature, applied magnetic field, but also on the amount of damage. Finally, a comparative study using Metropolis and Glauber dynamics indicates a slower decay rate of the average Hamming distance for the Glauber protocol.