Roughening transition in a one-dimensional growth process

A class of nonequilibrium models with short-range interactions and sequential updates is presented. The models describe one-dimensional growth processes which display a roughening transition between a smooth and a rough phase. This transition is accompanied by spontaneous symmetry breaking, which is described by an order parameter whose dynamics is nonconserving. Some aspects of models in this class are related to directed percolation in 1 + 1 dimensions, although unlike directed percolation the models have no absorbing states. Scaling relations are derived and compared with Monte Carlo simulations.