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. Some of the features of the roughening transition which takes place in these models are related to contact pr ocesses or directed percolation type problems. The models are analyzed using a mean field approximation, scaling arguments, and numerical si mulations. In the smooth phase the symmetry of the underlying dynamics is spontaneously broken. A family of order parameters which are not c onserved 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 the ory appropriate for studying the roughening transition is introduced a nd discussed.