Roughening Transition of a Restricted Solid-on-Solid Model in the Directed Percolation Universality Class

TL;DR

This paper investigates a restricted solid-on-solid growth model showing a roughening transition, analyzing its critical behavior, universality class, and order parameters, revealing complex phase structures and crossover phenomena.

Contribution

It introduces a finite-size scaling analysis of a growth model exhibiting a roughening transition within the directed percolation universality class, including critical exponents and phase characterization.

Findings

Critical exponent consistent with directed percolation

Disordered flat phase with antiferromagnetic structure

Crossover to KPZ behavior in rough phase

Abstract

We carried out a finite-size scaling analysis of the restricted solid-on-solid version of a recently introduced growth model that exhibits a roughening transition accompanied by spontaneous symmetry breaking. The dynamic critical exponent of the model was calculated and found to be consistent with the universality class of the directed percolation process in a symmetry-broken phase with a crossover to Kardar-Parisi-Zhang behavior in a rough phase. The order parameter of the roughening transition together with the string order parameter was calculated, and we found that the flat, gapped phase is disordered with an antiferromagnetic spin-fluid structure of kinks, although strongly dominated by the completely flat configuration without kinks. A possible interesting extension of the model is mentioned.