First-order phase transition with a logarithmic singularity in a model with absorbing states.

Recently, Lipowski [Phys. Rev. E 62, 4401 (2000)] investigated a stochastic lattice model which exhibits a discontinuous transition from an active phase into infinitely many absorbing states. Since the transition is accompanied by an apparent power-law singularity, it was conjectured that the model may combine features of first- and second-order phase transitions. In the present work it is shown that this singularity emerges as an artifact of the definition of the model in terms of products. Instead of a power law, we find a logarithmic singularity at the transition. Moreover, we generalize the model in such a way that the second-order phase transition becomes accessible. As expected, this transition belongs to the universality class of directed percolation.