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An Ising model for damage spreading with a probability of damage healing ($q= 1 - p$) is proposed and studied by means of Monte Carlo simulations. In thelimit $p \to 1$ the new model is mapped to the standard Ising model. It isfound that, for temperatures above the Onsager critical temperature ($T_{C}$),there exist a no trivial finite value of $p$ that sets the critical point($p_{c}$) for the onset of damage spreading. It is found that $p_{c}$ dependson $T$, defining a critical curve at the border between damage spreading anddamage healing. Transitions along such curve are found to belong to theuniversality class of directed percolation. The phase diagram of the model isalso evaluated showing that for large $T$ one has $p_{c} \propto (T-T_{C})^{\alpha}$, with $\alpha = 1$. Within the phase where the damage remainsactive, the stationary value of the damage depends lineally on both $p - p_{c}$and $T - T_{C} $.

A Model for Damage Spreading with Damage Healing: Monte Carlo Study of the two Dimensional Ising Ferromagnet