We study, through numerical simulations, the spreading of damage on the bi-dimensional ferromagnetic Ising model submitted to a new kind of external field h recently introduced in the literature in the context of cellular automata. The field h is defined as the frequency at which different random numbers are used for updating the two replicas. We show that h is the conjugate field to the Hamming distance, ie it destroys the dynamical continuous transition observed at h= 0, and the associated susceptibility diverges at the critical temperature.