Smooth Phases, Roughening Transitions and Novel Exponents in One-dimensional Growth Models

TL;DR

This paper investigates one-dimensional solid-on-solid growth models, revealing smooth and rough phases, analyzing the roughening transition with novel exponents, and introducing a field theory for these phenomena.

Contribution

It introduces a new class of growth models, analyzes their phase transition behavior, and identifies novel critical exponents and symmetry-breaking mechanisms.

Findings

Identification of smooth and rough phases in 1D growth models

Discovery of novel critical exponents at the roughening transition

Demonstration of continuous symmetry breaking in one dimension

Abstract

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.