First-order transition with power-law singularity in models with absorbingstates

We study one- and two-dimensional models which undergo a transition between active and absorbing phases. The transition point in these models is of a novel type: jump of the order parameter coincides with its power-law singul arity. Some arguments supported by Monte Carlo simulations prompted us to p redict the exact location of the transition point. Both models possess gaug elike symmetry.