First-order phase transition with a logarithmic singularity in a model with absorbing states - art. no. 016109

Recently, Lipowski [Phys. Rev. E 62, 4401 (2000)] investigated a stochastic lattice model which exhibits a discontinuous transition from an active pha se into infinitely many absorbing states. Since the transition is accompani ed by an apparent power-law singularity, it was conjectured that the model may combine features of first- and second-order phase transitions. In the p resent 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 f ind a logarithmic singularity at the transition. Moreover, we generalize th e model in such a way that the second-order phase transition becomes access ible. As expected, this transition belongs to the universality class of dir ected percolation.