Smooth phases, roughening transitions, and novel exponents in one-dimensional growth models

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 $d=1\mathrm{}$. 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.