Roughening Transition in a One-Dimensional Growth Process

TL;DR

This paper introduces a class of one-dimensional nonequilibrium growth models exhibiting a roughening transition, characterized by spontaneous symmetry breaking and analyzed through scaling relations and Monte Carlo simulations.

Contribution

It presents new models of 1D growth processes with a roughening transition and explores their symmetry-breaking behavior and relation to directed percolation.

Findings

Identification of a roughening transition in 1D growth models

Demonstration of spontaneous symmetry breaking at the transition

Validation of scaling relations via Monte Carlo simulations

Abstract

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 non-conserving. 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.