  We study the spreading of damage in the one-dimensional Ising model by means
of the stochastic dynamics resulting from coupling the system and its replica
by a family of algorithms that interpolate between the heat bath and the
Hinrichsen-Domany algorithms. At high temperatures the dynamics is exactly
mapped into de Domany-Kinzel probabilistic cellular automaton. Using a
mean-field approximation and Monte Carlo simulations we find the critical line
that separates the phase where the damage spreads and the one where it does
not.

Statistical Mechanics