Renormalization group study of one-dimensional systems with roughening transitions

TL;DR

This paper extends a real space renormalization group method to analyze one-dimensional surface growth models, successfully capturing complex phase behavior and roughening transitions related to directed percolation.

Contribution

The study generalizes and tests a renormalization technique on a new surface growth model, revealing detailed phase diagrams and critical exponents in one dimension.

Findings

Accurately reproduces phase diagram and roughness exponents

Identifies the separatrix among different phases

Demonstrates the method's versatility and physical insights

Abstract

A recently introduced real space renormalization group technique, developed for the analysis of processes in the Kardar-Parisi-Zhang universality class, is generalized and tested by applying it to a different family of surface growth processes. In particular, we consider a growth model exhibiting a rich phenomenology even in one dimension. It has four different phases and a directed percolation related roughening transition. The renormalization method reproduces extremely well all the phase diagram, the roughness exponents in all the phases and the separatrix among them. This proves the versatility of the method and elucidates interesting physical mechanisms.