  A class of solid-on-solid growth models with short range interactions and
sequential updates is studied. The models exhibit both smooth and rough phases
in dimension d=1. Some of the features of the roughening transition which takes
place in these models are related to contact processes or directed percolation
type problems. The models are analyzed using a mean field approximation,
scaling arguments and numerical simulations. In the smooth phase the symmetry
of the underlying dynamics is spontaneously broken. A family of order
parameters which are not conserved by the dynamics is defined as well as
conjugate fields which couple to these order parameters. The corresponding
critical behavior is studied and novel exponents identified and measured. We
also show how continuous symmetries can be broken in one dimension. A field
theory appropriate for studying the roughening transition is introduced and
discussed.
