We present a study of the influence of different types of disorder on systems
in the Ising universality class by employing both a dynamical field theory
approach and extensive Monte Carlo simulations. We reproduce some well known
results for the case of quenched disorder (random temperature and random
field), and analyze the effect of four different types of time-dependent
disorder scarcely studied so far in the literature. Some of them are of obvious
experimental and theoretical relevance (as for example, globally fluctuating
temperatures or random fields). All the predictions coming from our field
theoretical analysis are fully confirmed by extensive simulations in two and
three dimensions, and novel qualitatively different, non-Ising transitions are
reported. Possible experimental setups designed to explore the described
phenomenologies are also briefly discussed.Comment: Submitted to Phys. Rev. E. Rapid Comm. 4 page